Forcing clique immersions through chromatic number
Copyright policy )Forcing clique immersions through chromatic number
Building on recent work of Dvo����k and Yepremyan, we show that every simple graph of minimum degree $7t+7$ contains $K_t$ as an immersion and that every graph with chromatic number at least $3.54t + 4$ contains $K_t$ as an immersion. We also show that every graph on $n$ vertices with no stable set of size three contains $K_{2\lfloor n/5 \rfloor}$ as an immersion.
26 pages, 1 figure
Extremal problems in graph theory, Graph Immersions, Hadwiger’s conjecture, graph coloring, chromatic number, [MATH] Mathematics [math], Vertex degrees, [INFO] Computer Science [cs], Coloring of graphs and hypergraphs, FOS: Mathematics, Mathematics - Combinatorics, Combinatorics (math.CO), minimum degree, Hadwiger's conjecture
Extremal problems in graph theory, Graph Immersions, Hadwiger’s conjecture, graph coloring, chromatic number, [MATH] Mathematics [math], Vertex degrees, [INFO] Computer Science [cs], Coloring of graphs and hypergraphs, FOS: Mathematics, Mathematics - Combinatorics, Combinatorics (math.CO), minimum degree, Hadwiger's conjecture
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