Director of Research (if dissertation) or Advisor (if thesis)
Kostochka, Alexandr V.
Doctoral Committee Chair(s)
West, Douglas B.
Committee Member(s)
Methuku, Abhishek
Bradshaw, Peter
Department of Study
Mathematics
Discipline
Mathematics
Degree Granting Institution
University of Illinois Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Graph coloring
DP-coloring
Defective coloring
Edge-coloring
Abstract
This dissertation investigates several extremal problems in graph theory, focusing on graph density under vertex coloring constraints, and upper bounds on the number of colors required for injective edge-colorings in graphs with given maximum degree.
A graph $G$ is $k$-critical (list $k$-critical, DP $k$-critical) if $\chi(G)= k$ ($\chi_\ell(G)= k$, $\cDP(G)= k$) and for every proper subgraph $G'$ of $G$, $\chi(G')
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