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Relaxed Coloring of Sparse Graphs

Kopreski, Michael C
Abstract
A graph G is (d_1,d_2,… ,d_t)-colorable if its vertices may be partitioned into subsets V_1,V_2,...,V_t such that for each i, the maximum degree of the subgraph induced by V_i is at most d_i. We study this relaxed coloring of graphs with bounded maximum average degrees. Specifically, we use discharging and other methods to seek new upper and lower bounds for the maximum average degree of (1,1,0)-colorable graphs. We generalize this result to colorings of the type (1_1,1_2,...,1_a,0_1,...,0_b), improving the results by Dorbec, Kaiser, Montassier, and Raspaud (J. of Graph Theory, 2014) for a large class of colorings.
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2016-12-01
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Undergraduate Honors Theses
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Yu, Gexin
Li, Chi-Kwong
Erlich, Joshua
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Mathematics
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https://scholarworks.wm.edu/handle/internal/10361
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