Vertex decomposability of complexes associated to forests

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Singh Anurag

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Journal Paper

Paper Information

Journal: TRANSACTIONS ON COMBINATORICS Year:2022 | Volume:11 | Issue:1 Page(s): 1-13

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Information Journal Paper

Title

Vertex decomposability of complexes associated to forests

Author(s)

Singh Anurag | Issue Writer Certificate

Keywords

‎Bounded degree complex‎

‎non-cover complex‎

‎complex of directed trees‎

‎vertex decomposable complex‎

‎forests

Abstract

In this article‎, ‎we discuss the vertex decomposability of three well-studied simplicial complexes associated to forests‎. ‎In particular‎, ‎we show that the bounded degree complex of a forest and the complex of directed trees of a multidiforest is vertex decomposable‎. ‎We then prove that the non-cover complex of a forest is either contractible or homotopy equivalent to a sphere‎. ‎Finally we provide a complete characterization of forests whose non-cover complexes are vertex decomposable‎.

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