Eric Andrews

On Twin Edge Colorings of Graphs

Abstract A twin edge k-coloring of a graph G is a proper edge coloring of G with the elements of Zk so that the induced vertex coloring in which the color of a vertex v in G is the sum (in Zk) of the colors of the edges incident with v is a proper vertex coloring. The minimum k for which G has a twin edge k-coloring is called the twin chromatic index of G. Among the results presented are formulas for the twin chromatic index of each complete graph and each complete bipartite graph

Stars and Their k-Ramsey Numbers

For bipartite graphs F and H with Ramsey number

On eulerian irregularity in graphs

R(F, H) = n

On Eulerian walks in graphs

R(F,H)=n and an integer k with

On eulerian regular complete 5-partite graphs and a Cycle Decomposition Problem

2 \le k \le n

On a graph theoretic division algorithm and maximal decompositions of graphs

2≤k≤n, the k-Ramsey number of F and H is the minimum order of a balanced complete k-partite graph G for which every red-blue coloring of G results in a subgraph of G isomorphic to F all of whose edges are colored red or a subgraph isomorphic to H all of whose edges are colored blue. A formula is presented for the k-Ramsey number of every two stars