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Conditional colorings of graphs |
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| Authors: | Hong-Jian Lai Jianliang Lin Taozhi Shui |
| Institution: | a Department of Mathematics, West VirginiaUniversity, Morgantown, WV 26506, USA b Department of Mathematics, South China University of Technology, Guangzhou, PR China c Department of Mathematics, Jinan University, Guangzhou 510632, PR China d College of Science, Chongqing Technology and Business University, Chongqing 400067, PR China |
| Abstract: | 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 to vertices with at least r different colors. The smallest integer k for which a graph G has a conditional (k,r)-coloring is the rth order conditional chromatic number χr(G). In this paper, the behavior and bounds of conditional chromatic number of a graph G are investigated. |
| Keywords: | Conditional coloring Conditional chromatic number |
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