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Vertex decompositions of two-dimensional complexes and graphs

2010/07/22 by Michał Adamaszek, Michal Adamaszek, Adamaszek, Michal
Computer Science · Mathematics · #05E45 #52C45 #68R10 #Advanced Graph Theory Research #Combinatorics (math.CO) #Digital Image Processing Techniques #FOS: Mathematics #Topological and Geometric Data Analysis #math.CO #msc:05E45 #msc:52C45 #msc:68R10

paper · pdf · doi:10.48550/arxiv.1007.4019

Improved presentation and fixed some bugs

openalex publication_date 2010/07/22 · arxiv created 2011/02/21 · arxiv updated 2011/02/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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