We study the problem of recognizing graph powers and computing roots of graphs. We provide a polynomial time recognition algorithm for r-th powers of graphs of girth at least 2r + ...
A proper coloring of the edges of a graph G is called acyclic if there is no 2-colored cycle in G. The acyclic edge chromatic number of G, denoted by a (G), is the least number of...
We present a simple and efficient algorithm for randomly generating simple graphs without small cycles. These graphs can be used to design high performance Low-Density Parity-Chec...
The aim of this paper is to give a coherent account of the problem of constructing cubic graphs with large girth. There is a well-defined integer µ0(g), the smallest number of v...
Let ;k g be the class of k-connected cubic graphs of girth at least g. For several choices of k and g, we determine a set Ok g of graph operations, for which, if G and H are graph...