Given a bipartite graph G with n nodes, m edges, and maximum degree โฌ, we ลฝ . find an edge-coloring for G using โฌ colors in time T q O m log โฌ , where T is the time needed to find a perfect matching in a k-regular bipartite graph with ลฝ . O m edges and k F โฌ. Together with best known bounds for T th
Edge covering coloring of nearly bipartite graphs
โ Scribed by Jihui Wang; Xia Zhang; Guizhen Liu
- Publisher
- Springer-Verlag
- Year
- 2006
- Tongue
- English
- Weight
- 184 KB
- Volume
- 22
- Category
- Article
- ISSN
- 1598-5865
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## Abstract Given a bipartite graph __G__(__U__โช__V, E__) with __n__ vertices on each side, an independent set __I__โ__G__ such that |__U__โฉ__I__|=|__V__โฉ__I__| is called a balanced bipartite independent set. A balanced coloring of __G__ is a coloring of the vertices of __G__ such that each color c
If the vertices of a graph G are partitioned into k classes V~, I/2 ..... Vk such that each V~ is an independent set and I1V~I-IV~[I ~< 1 for all i#j, then G is said to be equitably colored with k colors. The smallest integer n for which G can be equitably colored with n colors is called the equitab