1 votes 1 votes Consider a complete bipartite graph $k_{m,n}$. For which values of $m$ and $n$ does this, complete graph have a Hamilton circuit $m = 3, n = 2$ $m = 2, n = 3$ $m = n > 2$ $m = n > 3$ Graph Theory ugcnetcse-june2014-paper2 graph-theory hamiltonian-graph + – makhdoom ghaya asked Jun 27, 2016 retagged Jul 8, 2016 by Arjun makhdoom ghaya 7.0k views answer comment Share Follow See all 0 reply Please log in or register to add a comment.
Best answer 5 votes 5 votes Km,n has a Hamilton circuit if and only if m=n>2 Digvijay Pandey answered Jun 27, 2016 selected Jul 8, 2016 by Arjun Digvijay Pandey comment Share Follow See all 4 Comments See all 4 4 Comments reply Neeraj Singh commented Jul 15, 2016 reply Follow Share K22 also has Hamilton circuit then why >2.It can be = also. 1 votes 1 votes LeenSharma commented Jul 15, 2016 i edited by LeenSharma Jul 15, 2016 reply Follow Share Neeraj Singh do you know what is circuit? 0 votes 0 votes Sushant Gokhale commented Sep 11, 2016 reply Follow Share @leensharma. Yes, Neeraj is right. K22 also contains hamiltonian ckt. But the questions asks that which is the most appropriate option. It doesnt state any fact. 0 votes 0 votes Neeraj Singh commented Dec 4, 2016 reply Follow Share yes I know. Circuit is path similar to a cycle that starts and ends at the same vertex. K22 also contains hamiltonian ckt. 0 votes 0 votes Please log in or register to add a comment.
0 votes 0 votes There should be equal vertices in both the partitions, and the count of each partition should be at least 2. So for $K_{m,n}$, $m=n\geq 2$ Option C is the closest match. JashanArora answered Dec 11, 2019 JashanArora comment Share Follow See all 0 reply Please log in or register to add a comment.