Adamaszek, Michał (2012) Vertex decompositions of two-dimensional complexes and graphs. Contributions to Discrete Mathematics, Volume 7 (Number 2). pp. 84-96.

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Abstract

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.

Item Type:	Journal Article
Alternative Title:
Divisions:	Faculty of Science, Engineering and Medicine > Science > Mathematics
Journal or Publication Title:	Contributions to Discrete Mathematics
Publisher:	University of Calgary * Department of Mathematics and Statistics
ISSN:	1715-0868
Official Date:	2012
Volume:	Volume 7
Number:	Number 2
Page Range:	pp. 84-96
Status:	Peer Reviewed
Publication Status:	Published
Access rights to Published version:	Restricted or Subscription Access

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