Vertex decompositions of two-dimensional complexes and graphs

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Certain families of two-dimensional simplicial complexes are defined by specific vertex decompositions, and their combinatorial properties are explored.
NP-completeness is established for determining if a graph can be reduced to a discrete graph by removing vertices of degree 3.
The exploration involves nonevasive and strongly collapsible complexes, highlighting their complex recognition problems.
Findings demonstrate connections between complex structures and analogous decomposition techniques in graph theory.

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Research investigates vertex decompositions in two-dimensional complexes and graphs, highlighting NP-completeness in some recognition problems.

Michał Adamaszek (2012) studied this question.

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Research investigates vertex decompositions in two-dimensional complexes and graphs, highlighting NP-completeness in some recognition problems.