A cycle cover of a graph is a spanning subgraph each node of which is part of exactly one simple cycle. A k-cycle cover is a cycle cover where each cycle has length at least k. Gi...
We present an algorithm for finding shortest surface non-separating cycles in graphs embedded on surfaces in O(g3/2 V 3/2 log V + g5/2 V 1/2 ) time, where V is the number of vert...
Let m1, m2, . . . , mt be a list of integers. It is shown that there exists an integer N such that for all n ≥ N, the complete graph of order n can be decomposed into edge-disjo...
We prove that for every c > 0 there exists a constant K = K(c) such that every graph G with n vertices and minimum degree at least cn contains a cycle of length t for every even...
Sufficient degree conditions for the existence of properly edge-colored cycles and paths in edge-colored graphs, multigraphs and random graphs are inverstigated. In particular, we...
A. Abouelaoualim, Kinkar Chandra Das, Wenceslas Fe...