Incremental construction properties in dimension two-shellability, extendable shellability and vertex decomposability

Sonoko Moriyama; Fumihiko Takeuchi

doi:10.1016/S0012-365X(02)00771-9

Incremental construction properties in dimension two-shellability, extendable shellability and vertex decomposability

Sonoko Moriyama, Fumihiko Takeuchi

INF - System Information Sciences

Research output: Contribution to journal › Article › peer-review

8 Citations (Scopus)

Abstract

We give new examples of shellable, but not extendably shellable two-dimensional simplicial complexes. They include minimal examples that are smaller than those previously known. We also give new examples of shellable, but not vertex decomposable two-dimensional simplicial complexes, including extendably shellable ones. This shows that neither extendable shellability nor vertex decomposability implies the other. We found these examples by enumerating shellable two-dimensional simplicial complexes that are not pseudomanifolds.

Original language	English
Pages (from-to)	295-296
Number of pages	2
Journal	Discrete Mathematics
Volume	263
Issue number	1-3
DOIs	https://doi.org/10.1016/S0012-365X(02)00771-9
Publication status	Published - 2003 Feb 28

Keywords

Combinatorial topology
Enumeration
Extendable shellability
Incremental construction
Shellability
Vertex decomposability

ASJC Scopus subject areas

Theoretical Computer Science
Discrete Mathematics and Combinatorics

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10.1016/S0012-365X(02)00771-9

Cite this

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abstract = "We give new examples of shellable, but not extendably shellable two-dimensional simplicial complexes. They include minimal examples that are smaller than those previously known. We also give new examples of shellable, but not vertex decomposable two-dimensional simplicial complexes, including extendably shellable ones. This shows that neither extendable shellability nor vertex decomposability implies the other. We found these examples by enumerating shellable two-dimensional simplicial complexes that are not pseudomanifolds.",

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N2 - We give new examples of shellable, but not extendably shellable two-dimensional simplicial complexes. They include minimal examples that are smaller than those previously known. We also give new examples of shellable, but not vertex decomposable two-dimensional simplicial complexes, including extendably shellable ones. This shows that neither extendable shellability nor vertex decomposability implies the other. We found these examples by enumerating shellable two-dimensional simplicial complexes that are not pseudomanifolds.

AB - We give new examples of shellable, but not extendably shellable two-dimensional simplicial complexes. They include minimal examples that are smaller than those previously known. We also give new examples of shellable, but not vertex decomposable two-dimensional simplicial complexes, including extendably shellable ones. This shows that neither extendable shellability nor vertex decomposability implies the other. We found these examples by enumerating shellable two-dimensional simplicial complexes that are not pseudomanifolds.

KW - Combinatorial topology

KW - Enumeration

KW - Extendable shellability

KW - Incremental construction

KW - Shellability

KW - Vertex decomposability

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JO - Discrete Mathematics

JF - Discrete Mathematics

SN - 0012-365X

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ER -

Incremental construction properties in dimension two-shellability, extendable shellability and vertex decomposability

Abstract

Keywords

ASJC Scopus subject areas

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