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이산수학 그룹
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Domination numbers and noncover complexes of hypergraphs

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Title
Domination numbers and noncover complexes of hypergraphs
Author(s)
Jinha Kim; Minki Kim
Publication Date
2021-05
Journal
JOURNAL OF COMBINATORIAL THEORY SERIES A, v.180
Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
Abstract
Let H be a hypergraph on a finite set V. A cover of H is a set of vertices that meets all edges of H. If W is not a cover of H, then W is said to be a noncover of H. The noncover complex of H is the abstract simplicial complex whose faces are the noncovers of H. In this paper, we study homological properties of noncover complexes of hypergraphs. In particular, we obtain an upper bound on their Leray numbers. The bound is in terms of hypergraph domination numbers. Also, our proof idea is applied to compute the homotopy type of the noncover complexes of certain uniform hypergraphs, called tight paths and tight cycles. This extends to hypergraphs known results on graphs. (C) 2021 Elsevier Inc. All rights reserved.
URI
https://pr.ibs.re.kr/handle/8788114/10034
DOI
10.1016/j.jcta.2021.105408
ISSN
0097-3165
Appears in Collections:
Pioneer Research Center for Mathematical and Computational Sciences(수리 및 계산과학 연구단) > Discrete Mathematics Group(이산 수학 그룹) > 1. Journal Papers (저널논문)
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