[PAST EVENT] Honors Thesis Defense: Michael Kopreski
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 prove that if maximum average degree of a graph is at most 4a/3+b, then it is (1_1,1_2,...,1_a,0_1,...,0_b)-colorable. This improves some result by Dorbec, Kaiser, Montassier, and Raspaud (2014, Journal of Graph Theory).