Vertex decompositions of two-dimensional complexes and graphs

Details Vertex decompositions of two-dimensional complexes and graphs Vertex decompositions of two-dimensional complexes and graphs

2010-07-22

arxiv.org/abs/1007.4019v2

Mathematics

Combinatorics

Improved presentation and fixed some bugs

Scientific paper

We investigate families of two-dimensional simplicial complexes defined in terms of vertex decompositions. They include nonevasive complexes, strongly collapsible complexes of Barmak and Miniam and analogues of 2-trees of Harary and Palmer. We investigate the complexity of recognition problems for those families and some of their combinatorial properties. Certain results follow from analogous decomposition techniques for graphs. For example, we prove that it is NP-complete to decide if a graph can be reduced to a discrete graph by a sequence of removals of vertices of degree 3.

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