Indivisibility for Classes of Graphs
Abstract
We examine indivisibility for classes of graphs. We show that the class of hereditarily α-sparse graphs is indivisible if and only if α > 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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