GATE Overflow for GATE CSE - Recent questions tagged graph-matching
https://gateoverflow.in/tag/graph-matching
Powered by Question2AnswerTIFR CSE 2022 | Part B | Question: 2
https://gateoverflow.in/382007/tifr-cse-2022-part-b-question-2
<p>Let $G=(V, E)$ be an undirected simple graph. A subset $M \subseteq E$ is a <em>matching</em> in $G$ if distinct edges in $M$ do not share a vertex. A matching is <em>maximal </em>if no strict superset of $M$ is a matching. How many maximal matchings does the following graph have?</p>
<p><img alt="" src="https://gateoverflow.in/?qa=blob&qa_blobid=12788851749305281586"></p>
<ol start="1" style="list-style-type:upper-alpha">
<li>$1$</li>
<li>$2$</li>
<li>$3$</li>
<li>$4$</li>
<li>$5$</li>
</ol>Graph Theoryhttps://gateoverflow.in/382007/tifr-cse-2022-part-b-question-2Thu, 01 Sep 2022 17:42:50 +0000TIFR CSE 2022 | Part B | Question: 6
https://gateoverflow.in/382003/tifr-cse-2022-part-b-question-6
<p>We are given a graph $G$ along with a matching $M$ and a vertex cover $C$ in it such that $|M|=|C|$. Consider the following statements:</p>
<ol>
<li>$M$ is a maximum matching in $G$.</li>
<li>$C$ is a minimum vertex cover in $G$.</li>
<li>$G$ is a bipartite graph.</li>
</ol>
<p>Which of the following is $\text{TRUE}$?</p>
<ol start="1" style="list-style-type:upper-alpha">
<li>Only statement $(1)$ is correct</li>
<li>Only statement $(2)$ is correct</li>
<li>Only statement $(3)$ is correct</li>
<li>Only statements $(1)$ and $(2)$ are correct</li>
<li>All the three statements $(1), (2),$ and $(3)$ are correct</li>
</ol>Graph Theoryhttps://gateoverflow.in/382003/tifr-cse-2022-part-b-question-6Thu, 01 Sep 2022 17:42:49 +0000Best Open Video Playlist for Graph Theory: Matching Topic | Discrete Mathematics
https://gateoverflow.in/380466/video-playlist-graph-theory-matching-discrete-mathematics
<p>Please list out the best free available video playlist for <strong>Graph Theory: Matching </strong>Topic from Discrete Mathematics as an answer here (only one playlist per answer). We'll then select the best playlist and add to <a href="http://classroom.gateoverflow.in" rel="nofollow">GO classroom</a> video lists. You can add any video playlist link including your own (as long as they are free to access) but standard ones are more likely to be selected as best.<br>
<br>
For the full list of selected videos please see <a href="https://docs.google.com/spreadsheets/d/e/2PACX-1vQTEfCg28q1B_buKRxaVvUjN_CTu9UntAiqi9qBiZZesmJE6LnqfkuwxNQOsNcU1g/pubhtml" rel="nofollow">here</a></p>Study Resourceshttps://gateoverflow.in/380466/video-playlist-graph-theory-matching-discrete-mathematicsSun, 14 Aug 2022 19:24:13 +0000TIFR CSE 2021 | Part A | Question: 6
https://gateoverflow.in/358962/tifr-cse-2021-part-a-question-6
<p>A matching in a graph is a set of edges such that no two edges in the set share a common vertex. Let $G$ be a graph on $n$ $\textit{vertices}$ in which there is a subset $M$ of $m$ $\textit{edges}$ which is a matching. Consider a random process where each vertex in the graph is independently selected with probability $0< p< 1$ and let $B$ be the set of vertices so obtained. What is the probability that there exists at least one edge from the matching $M$ with both end points in the set $B$?</p>
<ol style="list-style-type:upper-alpha" type="A">
<li>$p^{2}$</li>
<li>$1-\left ( 1-p^{2} \right )^{m}$</li>
<li>$p^{2m}$</li>
<li>$\left ( 1-p^{2} \right )^{m}$</li>
<li>$1-\left ( 1-p\left ( 1-p \right ) \right )^{m}$</li>
</ol>Graph Theoryhttps://gateoverflow.in/358962/tifr-cse-2021-part-a-question-6Thu, 25 Mar 2021 09:16:23 +0000CMI2018-A-9
https://gateoverflow.in/320484/cmi2018-a-9
<p>Your college has sent a contingent to take part in a cultural festival at a neighbouring institution. Several team events are part of the programme. Each event takes place through the day with many elimination rounds. Your contingent is multi-talented and each individual has the skills to take part in a subset of the events. However, the same individual cannot be part of the team for two different events because of a possible clash in timings. Your aim is to create teams to take part in as many events as possible.</p>
<p>To do this, you decide to model the problem as a graph where the nodes are the events and edges represent pairs of events where the team that you plan to send shares a member. In this setting, the graph theoretic question to be answered is:</p>
<ol start="1" style="list-style-type:upper-alpha">
<li>Find a maximum length simple cycle</li>
<li>Find a maximum size independent set</li>
<li>Find a maximum matching</li>
<li>Find a maximal connected component</li>
</ol>Graph Theoryhttps://gateoverflow.in/320484/cmi2018-a-9Fri, 13 Sep 2019 14:34:29 +0000GeeksforGeeks
https://gateoverflow.in/301391/geeksforgeeks
<div class="panel panel-default" style="margin:5px;background-color:#f5f5f5">
<div class="problemQuestion panel-body" style="font-weight: 700;padding:10px;margin:20px;font-size:15px;">Let G be a graph with no isolated vertices, and let M be a maximum matching of G. For each vertex v not saturated by M, choose an edge incident to v. Let T be the set of all the chosen edges, and let L = M ∪ T. Which of the following option is TRUE?</div>
</div>
<div style="margin-left:20px;margin-top:15px;">
<div class="table-responsive">
<table>
<tbody>
<tr>
<td style="width:30px">
<div style="color: #fff;background: #00930E;width: 40px;height: 40px;display: block; border-radius: 40px; -moz-border-radius: 40px; -webkit-border-radius: 40px; -khtml-border-radius: 40px; font-size: 30px; line-height: 40px; text-decoration: none; text-align: center; font-family: Arial,Helvetica,">A</div>
</td>
<td><strong>L is always an edge cover of G.</strong></td>
</tr>
<tr>
<td style="width:30px">
<div style="color: #fff;background: #00930E;width: 40px;height: 40px;display: block; border-radius: 40px; -moz-border-radius: 40px; -webkit-border-radius: 40px; -khtml-border-radius: 40px; font-size: 30px; line-height: 40px; text-decoration: none; text-align: center; font-family: Arial,Helvetica,">B</div>
</td>
<td><strong>L is always a minimum edge cover of G.</strong></td>
</tr>
<tr>
<td style="width:30px">
<div style="color: #fff;background: #00930E;width: 40px;height: 40px;display: block; border-radius: 40px; -moz-border-radius: 40px; -webkit-border-radius: 40px; -khtml-border-radius: 40px; font-size: 30px; line-height: 40px; text-decoration: none; text-align: center; font-family: Arial,Helvetica,">C</div>
</td>
<td><strong>Both (A) and (B)</strong></td>
</tr>
<tr>
<td style="width:30px">
<div style="color: #fff;background: #00930E;width: 40px;height: 40px;display: block; border-radius: 40px; -moz-border-radius: 40px; -webkit-border-radius: 40px; -khtml-border-radius: 40px; font-size: 30px; line-height: 40px; text-decoration: none; text-align: center; font-family: Arial,Helvetica,">D</div>
</td>
<td><strong>Neither (A) nor (B)</strong></td>
</tr>
</tbody>
</table>
</div>
</div>
<p> </p>
<p>Can anyone pls help solving this?</p>Graph Theoryhttps://gateoverflow.in/301391/geeksforgeeksWed, 30 Jan 2019 16:42:45 +0000Gateforum Test Series: Graph Theory - Graph Matching
https://gateoverflow.in/288108/gateforum-test-series-graph-theory-graph-matching
<p><img alt="" src="https://gateoverflow.in/?qa=blob&qa_blobid=16835915087140077554"></p>
<p> </p>Graph Theoryhttps://gateoverflow.in/288108/gateforum-test-series-graph-theory-graph-matchingWed, 02 Jan 2019 11:27:37 +0000Zeal Test Series 2019: Graph Theory - Graph Matching
https://gateoverflow.in/282299/zeal-test-series-2019-graph-theory-graph-matching
<p style="text-align:center"><img alt="" src="https://gateoverflow.in/?qa=blob&qa_blobid=14864192867657094684"></p>
<p> </p>Graph Theoryhttps://gateoverflow.in/282299/zeal-test-series-2019-graph-theory-graph-matchingFri, 21 Dec 2018 19:32:57 +0000Complete Matching
https://gateoverflow.in/252776/complete-matching
<p style="text-align:center"><img alt="" src="https://gateoverflow.in/?qa=blob&qa_blobid=15304933682884591739"></p>
<p>Consider the Bipartite graph shown. If four edges are chosen at random, what is the probability that they form a complete matching from V1 to V2 ?</p>
<p>A. 0.039</p>
<p>B. 0.052</p>
<p>C. 0.071</p>
<p>D. 0.083</p>Mathematical Logichttps://gateoverflow.in/252776/complete-matchingSat, 13 Oct 2018 05:30:06 +0000ACE Bits And Bytes
https://gateoverflow.in/227955/ace-bits-and-bytes
<h2>Number of perfect matching in W<sub>n </sub>(n>=4 and n is even) _________.</h2>Graph Theoryhttps://gateoverflow.in/227955/ace-bits-and-bytesMon, 23 Jul 2018 21:16:20 +0000Perfect Matching
https://gateoverflow.in/220278/perfect-matching
Perfect matching is a set of edges such that each vertex appears only once and all vertices appear at least once (EXACTLY one appearance). So for n vertices perfect matching will have n/2 edges and there won't be any perfect matching if n is odd.<br />
<br />
<br />
I don't know whether i got it properly or not. Can please anybody explain the Perfect matching in a complete graph with simpler examples ?Graph Theoryhttps://gateoverflow.in/220278/perfect-matchingSun, 10 Jun 2018 12:54:54 +0000Ace Test Series: Graph Theory - Matching
https://gateoverflow.in/197366/ace-test-series-graph-theory-matching
<p><img alt="" src="https://gateoverflow.in/?qa=blob&qa_blobid=2347703009055108745"></p>
<p>my answer is C</p>
<p>but the answer given is A</p>
<p>someone please explain</p>Graph Theoryhttps://gateoverflow.in/197366/ace-test-series-graph-theory-matchingSat, 20 Jan 2018 02:53:46 +0000graph theory
https://gateoverflow.in/184693/graph-theory
Maximum no of edges in a triangle-free, simple planar graph with 10 verticesGraph Theoryhttps://gateoverflow.in/184693/graph-theorySat, 23 Dec 2017 05:08:59 +0000Matchings in a Graph
https://gateoverflow.in/174992/matchings-in-a-graph
<p><img alt="" src="https://gateoverflow.in/?qa=blob&qa_blobid=1098626164388239596" style="float:left"></p>Graph Theoryhttps://gateoverflow.in/174992/matchings-in-a-graphTue, 28 Nov 2017 22:52:16 +0000chromatic number
https://gateoverflow.in/168890/chromatic-number
Let G be a planar Graph Such that every phase is bordered by exactly 3 edges which of the following can never be value for X(G)<br />
<br />
a)2 b)3 C)4 d)none of theseGraph Theoryhttps://gateoverflow.in/168890/chromatic-numberSat, 11 Nov 2017 10:56:00 +0000PERFECT MATCHING IN COMPLETE GRAPH
https://gateoverflow.in/166671/perfect-matching-in-complete-graph
<p><img alt="" src="https://gateoverflow.in/?qa=blob&qa_blobid=1116234532547906579"></p>Graph Theoryhttps://gateoverflow.in/166671/perfect-matching-in-complete-graphMon, 06 Nov 2017 01:02:54 +0000DISCRETE
https://gateoverflow.in/154041/discrete
Let T be a tree with n vertices and k be the maximum size of an independent set in T. Then the size of maximum matching in T is<br />
<br />
(A) k<br />
<br />
(B) n−k<br />
<br />
(C) (n−1)/2Graph Theoryhttps://gateoverflow.in/154041/discreteThu, 21 Sep 2017 12:13:05 +0000Graph Theory
https://gateoverflow.in/151990/graph-theory
Consider a 'reversed Kruskal' Algorithm for computing a MST. Initialize T to be the set of all edges in the graph. Now consider edges from largest to smallest cost. For each edge, delete it from T if that edge belongs to a cycle in T. Assuming all the edge costs are distinct, does this new algorithm correctly compute a MST?<br />
<br />
<br />
<br />
a) Yes<br />
<br />
b) no<br />
<br />
c) cant sayGraph Theoryhttps://gateoverflow.in/151990/graph-theoryWed, 13 Sep 2017 21:54:49 +0000[Discrete Maths] Graph Theory Rosen,Chromatic number
https://gateoverflow.in/132851/discrete-maths-graph-theory-rosen-chromatic-number
<p>What are the chromatic number of following graphs?</p>
<p><img alt="" src="https://gateoverflow.in/?qa=blob&qa_blobid=2427432278983743495"></p>
<p>Answer is 6 and 4 respectively.But i am getting 3 for both.</p>
<p>Please someone confirm this?</p>Mathematical Logichttps://gateoverflow.in/132851/discrete-maths-graph-theory-rosen-chromatic-numberMon, 12 Jun 2017 22:08:59 +0000[Discrete maths] graph theory Perfect matching
https://gateoverflow.in/132353/discrete-maths-graph-theory-perfect-matching
When matching number and covering number are same then can we say that it is a perfect matching case?Do i need to check the elements of the set( edges in both matching and covering) also if their cardinality is same?If yes,then can someone give me an example where matching number and covering number same but still it is not a perfect match?I am not able to find such a case and i think it will not exist.Mathematical Logichttps://gateoverflow.in/132353/discrete-maths-graph-theory-perfect-matchingThu, 08 Jun 2017 15:11:26 +0000narsingh deo
https://gateoverflow.in/119875/narsingh-deo
In a village there are equal no of boys and girls of marriageable age.Each boy dates a certain no. of girls and each girl dates a certain number of boys,under what condition is it possible that every girl and boy gets married to one of their dates?Graph Theoryhttps://gateoverflow.in/119875/narsingh-deoMon, 27 Feb 2017 03:49:57 +0000made easy
https://gateoverflow.in/62631/made-easy
<p>Please explain how perfect matching in given tree is 1?</p>
<p>Why not 3 with edges ab,ce,df?</p>
<p><img alt="" src="https://gateoverflow.in/?qa=blob&qa_blobid=4504020862575904538"></p>
Mathematical Logichttps://gateoverflow.in/62631/made-easyWed, 10 Aug 2016 08:13:04 +0000Virtual Gate Test Series: Discrete Mathematics - Graph Theory (Matching Number)
https://gateoverflow.in/37974/virtual-series-discrete-mathematics-theory-matching-number
<p>Find the matching number for the given graph-</p>
<p><img alt="" src="https://gateoverflow.in/?qa=blob&qa_blobid=11903843829953706322"></p>Graph Theoryhttps://gateoverflow.in/37974/virtual-series-discrete-mathematics-theory-matching-numberTue, 26 Jan 2016 14:43:20 +0000Finding matching number of graph
https://gateoverflow.in/36597/finding-matching-number-of-graph
<p><img alt="" src="https://gateoverflow.in/?qa=blob&qa_blobid=10063343342017607947"></p>
<p>Given explanation:</p>
<p><img alt="" src="https://gateoverflow.in/?qa=blob&qa_blobid=1899557196183761378"></p>
<p>In the above explanation, it is written that matching number is 4 but I am getting matching number as 3 for this graph(choosing edges 1-2, 3-4 and 6-7). Please check where I am going wrong</p>
Graph Theoryhttps://gateoverflow.in/36597/finding-matching-number-of-graphMon, 18 Jan 2016 21:47:35 +0000TIFR CSE 2012 | Part B | Question: 20
https://gateoverflow.in/26480/tifr-cse-2012-part-b-question-20
<p>This question concerns the classes $P$ and $NP.$ If you are familiar with them, you may skip the definitions and go directly to the question.<br>
Let $L$ be a set. We say that $L$ is in $P$ if there is some algorithm which given input $x$ decides if $x$ is in $L$ or not in time bounded by a polynomial in the length of $x.$ For example, the set of all connected graphs is in $P,$ because there is an algorithm which, given a graph graph, can decide if it is connected or not in time roughly proportional to the number of edges of the graph.</p>
<p>The class $NP$ is a superset of class $P.$ It contains those sets that have membership witnesses that can be verified in polynomial time. For example, the set of composite numbers is in $NP.$ To see this take the witness for a composite number to be one of its divisors. Then the verification process consists of performing just one division using two reasonable size numbers. Similarly, the set of those graphs that have a Hamilton cycle, i.e. a cycle containing all the vertices of the graph, is in in $NP.$ To verify that the graph has a Hamilton cycle we just check if the witnessing sequence of vertices indeed a cycle of the graph that passes through all the vertices of the graph. This can be done in time that is polynomial in the size of the graph.</p>
<p>More precisely, if $L$ is a set in $P$ consisting of elements of the form $(x, w),$ then the set $$M = \{x : \exists w, |w| ≤ |x|^k\text{ and }(x, w) \in L\},$$<br>
is in N P .<br>
Let $G = (V, E)$ be a graph. $G$ is said to have perfect matching if there is a subset $M$ of the edges of $G$ so that</p>
<ol style="list-style-type:lower-roman">
<li>No two edges in $M$ intersect (have a vertex in common); and</li>
<li>Every vertex of $G$ has an edge in $M.$</li>
</ol>
<p>Let $\text{MATCH}$ be the set of all graphs that have a perfect matching. Let $\overline{\text{MATCH}}$ be the set of graphs that do not have a perfect matching. Let $o(G)$ be the number of components of $G$ that have an odd number of vertices.</p>
<p>$\text{Tutte’s Theorem:}$ $G \in \text{MATCH}$<em> </em>if and only if for all subsets $S$ of $V,$ the number of components in $G − S$ (the graph formed by deleting the vertices in $S)$ with an odd number of vertices is at most $|S|.$ That is, $$G \in \text{MATCH} ↔ \forall S \subseteq V o(G − S) \leq |S|.$$</p>
<p>Which of the following is true?</p>
<ol style="list-style-type:upper-alpha">
<li>$\text{MATCH} ∈ NP\text{ and }\overline{\text{MATCH}} \notin NP$</li>
<li>$\overline{\text{MATCH}} ∈ NP\text{ and }\text{MATCH} \notin NP$</li>
<li>$\text{MATCH} ∈ NP\text{ and }\overline{\text{MATCH}} ∈ NP$</li>
<li>$\text{MATCH} \notin P\text{ and } \overline{\text{MATCH}} \notin P$</li>
<li>none of the above</li>
</ol>Graph Theoryhttps://gateoverflow.in/26480/tifr-cse-2012-part-b-question-20Sat, 14 Nov 2015 18:47:40 +0000no of perfect matching in complete graph
https://gateoverflow.in/4788/no-of-perfect-matching-in-complete-graph
<p>Is there a way to find no of perfect matchings in a complete graph K<sub>n </sub>where n could be either even or odd..?</p>
Graph Theoryhttps://gateoverflow.in/4788/no-of-perfect-matching-in-complete-graphTue, 02 Dec 2014 01:16:43 +0000GATE CSE 2003 | Question: 36
https://gateoverflow.in/926/gate-cse-2003-question-36
<p>How many perfect matching are there in a complete graph of $6$ vertices?</p>
<ol style="list-style-type:upper-alpha">
<li>$15$</li>
<li>$24$</li>
<li>$30$</li>
<li>$60$</li>
</ol>Graph Theoryhttps://gateoverflow.in/926/gate-cse-2003-question-36Tue, 16 Sep 2014 18:06:22 +0000