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32.784  Articles
1 of 3.279 pages  |  10  records  |  more records»
A star coloring of a graph G is a proper vertex coloring in which every path on four vertices in G is not bicolored. The star chromatic number ?s (G) of G is the least number of colors needed to star color G. In this paper, we have generalized the star ch... see more

A star edge coloring of a graph G is a proper edge coloring without bichromatic paths and cycles of length four. In this paper, we obtain the star edge chromatic number of the corona product of path with cycle, path with wheel, path with helm and path wit... see more

In a search for triangle-free graphs with arbitrarily large chromatic numbers, Mycielski developed a graph transformation that transforms a graph G into a new graph µ(G), we now call the Mycielskian of G, which has the same clique number as G and whose ch... see more

Let s and k be positive integers with k = 2 and G1, G2, …, Gk be simple graphs. The set multipartite Ramsey number, denoted by Ms(G1, G2, …, Gk), is the smallest positive integer c such that any&... see more

Abstract: Let the star on n vertices, namely K1, n - 1 be denoted by Sn. If every two coloring of the edges of a complete balanced multipartite graph Kj × s there is a copy of Sn in the first color or a copy of... see more

Let k = 2 be an integer and G be a connected graph of order at least 3. A twin k-edge coloring of G is a proper edge coloring of G that uses colors from Zk and that induces a proper vertex colori... see more

For simple graphs G and H the size multipartite Ramsey number mj(G,H) is the smallest natural number t such that any arbitrary red-blue coloring on the edges of Kjxt contains a red G or a blue H as a subgraph. We studied the size tripartite Ramsey numbers... see more

Burger and Vuuren defined the size multipartite Ramsey number for a pair of complete, balanced, multipartite graphs mj(Kaxb,Kcxd), for natural numbers a,b,c,d and j, where a,c >= 2, in 2004. They have also determined the necessary and sufficient condit... see more

We define a new type of vertex coloring which generalizes vertex coloring in graphs, hypergraphs, and simplicial complexes. This coloring also generalizes oriented coloring, acyclic coloring, and star coloring. There is an associated symmetric function in... see more

1 of 3.279 pages  |  10  records  |  more records»