For an undirected graph ¢ without self-loop, we prove: (i) that the number of closed patterns in the adjacency matrix of ¢ is even; (ii) that the number of the closed patterns i...
Given an undirected graph with edge weights, we are asked to find an orientation, i.e., an assignment of a direction to each edge, so as to minimize the weighted maximum outdegree...
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...