3 votes 3 votes For which values of $m$ and $n$ does the complete bipartite graph $k_{m,n}$ have a Hamiltonian circuit ? $m\neq n,\ \ m,n \geq 2$ $m\neq n,\ \ m,n \geq 3$ $m=n,\ \ m,n \geq 2$ $m= n,\ \ m,n \geq 3$ Graph Theory ugcnetcse-june2019-paper2 graph-theory + – Arjun asked Jul 2, 2019 edited Jul 24, 2019 by Lakshman Bhaiya Arjun 2.1k views answer comment Share Follow See 1 comment See all 1 1 comment reply srestha commented Jul 2, 2019 reply Follow Share $3)$ and $4)$ both ans here. Formula Complete Bipartite Graph $K_{n,n}$ 0 votes 0 votes Please log in or register to add a comment.
4 votes 4 votes Option $3.$ is the correct answer. (Option $4.$ is also correct but option $3$ is more appropriate since it covers the case $m,n = 2$) For a bipartite graph($K_{m,n}$) to be a hamiltonian graph $m=n$ and $m,n\geq 2$ https://math.stackexchange.com/questions/1064178/proof-of-hamilton-cycle-in-a-complete-bipartite-graph Satbir answered Jul 3, 2019 Satbir comment Share Follow See all 0 reply Please log in or register to add a comment.
0 votes 0 votes Option D k2 there is no Hamiltonian circuit K3 onwards Hamiltonian circuit is possible K2 Hamiltonian path Raghava45 answered Sep 17, 2019 Raghava45 comment Share Follow See all 0 reply Please log in or register to add a comment.