Recent questions tagged graph-matching

Let $G$ be an undirected graph, which is a path on $8$ vertices. The number of matchings in $G$ is $\_\_\_\_$. (answer in integer)

You are starting a new bus service. You are hiring drivers and conductors. A driver and a conductor can run a bus only if they can speak a common language. There are $n$ ...

Consider the following statements:$\text{P}$: There exists no simple, undirected and connected graph with $80$ vertices and $77$ edges.$\text{Q}$: All vertices of Euler g...

Count the number of perfect matchings in the bipartite graph whose adjacency matrix $\text{A}$ is as follows.\[\left[\begin{array}{lll}1 & 1 & 0 \\0 & 1 & 1 \\1 & 1 & 1\e...

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:$M$ is a maximum matching in $G$.$C...

For the following graph, what is the summation of chromatic number and matching number?

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 plac...

Number of perfect matching in Wn (n>=4 and n is even) _________.

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 match...

my answer is Cbut the answer given is Asomeone please explain

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(A) k(B) n−k(C) (n−1)/2

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 e...

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 an...