Independence complexes of strongly orderable graphs

Authors : Mehmet Akif YETİM

Pages : 445-455

Doi:10.31801/cfsuasmas.874855

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Publication Date : 2022-06-30

Article Type : Research Paper

Abstract :We prove that for any finite strongly orderable insert ignore into journalissuearticles values(generalized strongly chordal); graph G , the independence complex Indinsert ignore into journalissuearticles values( G ); is either contractible or homotopy equivalent to a wedge of spheres of dimension at least bpinsert ignore into journalissuearticles values( G );−1, where bpinsert ignore into journalissuearticles values( G ); is the biclique vertex partition number of G . In particular, we show that if G is a chordal bipartite graph, then Indinsert ignore into journalissuearticles values( G ); is either contractible or homotopy equivalent to a sphere of dimension at least bpinsert ignore into journalissuearticles values( G ); − 1.
Keywords : Independence complex, strongly orderable, strongly chordal, chordal bipartite, convex bipartite, homotopy type, biclique vertex partition