Indivisibility for Classes of Graphs (2312.01466v2)

Published 3 Dec 2023 in math.CO and math.LO

Abstract: We examine indivisibility for classes of graphs. We show that the class of hereditarily $\alpha$-sparse graphs is indivisible if and only if $\alpha > 2$. Additionally, we show that the following classes of graphs are indivisible: perfect graphs, cographs, and chordal graphs, and the following classes of graphs are not indivisible: threshold graphs, split graphs, and distance-hereditary graphs.

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