We present an infinite family of 3-connected non-bipartite graphs with chromatic roots in the interval (1, 2) thus resolving a conjecture of Jackson’s in the negative. In addit...
In this paper we further investigate the well-studied problem of finding a perfect matching in a regular bipartite graph. The first non-trivial algorithm, with running time O(mn),...
Let Kn,n denote the complete bipartite graph with n vertices in each partite set and Kn,n +I denote Kn,n with a 1-factor added. It is proved in this paper that there exists an m-c...
We prove that it is NP-complete to decide whether a bipartite graph of maximum degree three on nk vertices can be partitioned into n paths of length k. Finally, we propose some ap...