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...
For an integer r > 0, a conditional (k, r)-coloring of a graph G is a proper k-coloring of the vertices of G such that every vertex of degree at least r in G will be adjacent t...
Hong-Jian Lai, Jianliang Lin, Bruce Montgomery, Ta...
A biclique is a complete bipartite subgraph of a graph. This paper investigates the fractional biclique cover number, bc(G), and the fractional biclique partition number, bp(G), o...
: This article proves the following result: Let G and G be graphs of orders n and n , respectively. Let G be obtained from G by adding to each vertex a set of n degree 1 neighbors....
We present a reduction method that reduces a graph to a smaller core graph which behaves invariant with respect to planarity measures like crossing number, skewness, and thickness....