A graph is equitably \(k\)-colorable if its vertices can be partitioned into \(k\) independent sets of as near equal sizes as possible. Regarding a non-null tree \(T\) as a bipartite graph \(T(X, Y)\), we show that \(T\) is equitably \(k\)-colorable if and only if (i) \(k \geqslant 2\) when ||\(X|-|
Equitable and proportional coloring of trees
✍ Scribed by Béla Bollobás; Richard K Guy
- Book ID
- 103506062
- Publisher
- Elsevier Science
- Year
- 1983
- Tongue
- English
- Weight
- 449 KB
- Volume
- 34
- Category
- Article
- ISSN
- 0095-8956
No coin nor oath required. For personal study only.
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## Abstract Given lists of available colors assigned to the vertices of a graph __G__, a __list coloring__ is a proper coloring of __G__ such that the color on each vertex is chosen from its list. If the lists all have size __k__, then a list coloring is __equitable__ if each color appears on at mo
Let \(\Delta(G)\) denote the maximum degree of a graph \(G\). The equitable \(\Delta\)-coloring conjecture asserts that a connected graph \(G\) is equitably \(\Delta(G)\)-colorable if it is different from \(K_{m}, C_{2 m+1}\) and \(K_{2 m+1,2 m+1}\) for all \(m \geqslant 1\). This conjecture is esta