For all integers k 3, we give an O(n4 ) time algorithm for the problem whose instance is a graph G of girth at least k together with k vertices and whose question is "Does G...
A (k; g)-graph is a k-regular graph with girth g. A (k; g)-cage is a (k; g)-graph with the least number of vertices. In this note, we show that (k; g)-cage has an r-factor of girt...
In the Connected Dominating Set problem we are given as input a graph G and a positive integer k, and are asked if there is a set S of at most k vertices of G such that S is a dom...
Jeager et al introduced a concept of group connectivity as an generalization of nowhere zero flows and its dual concept group coloring, and conjectured that every 5-edge connected...