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- W2080846906 abstract "An equitable coloring of a graph is a proper vertex coloring such that the sizes of any two color classes differ by at most 1. A d-degenerate graph is a graph G in which every subgraph has a vertex with degree at most d. A star Sm with m rays is an example of a 1-degenerate graph with maximum degree m that needs at least 1+m/2 colors for an equitable coloring. Our main result is that every n-vertex d-degenerate graph G with maximum degree at most n/15 can be equitably k-colored for each $k ge 16d$. The proof of this bound is constructive. We extend the algorithm implied in the proof to an O(d)-factor approximation algorithm for equitable coloring of an arbitraryd -degenerate graph. Among the implications of this result is an O(1)-factor approximation algorithm for equitable coloring of planar graphs with fewest colors. A variation of equitable coloring (equitable partitions) is also discussed." @default.
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- W2080846906 date "2005-01-01" @default.
- W2080846906 modified "2023-10-09" @default.
- W2080846906 title "On Equitable Coloring of <i>d</i>-Degenerate Graphs" @default.
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- W2080846906 doi "https://doi.org/10.1137/s0895480103436505" @default.
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