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Graphs without two vertex-disjoint S-cycles
- Authors
- Kang, Minjeong; Kwon, O jung; Lee, Myounghwan
- Issue Date
- Oct-2020
- Publisher
- ELSEVIER
- Keywords
- Erdos–Posa property; S-cycle
- Citation
- DISCRETE MATHEMATICS, v.343, no.10, pp.1 - 18
- Indexed
- SCIE
SCOPUS
- Journal Title
- DISCRETE MATHEMATICS
- Volume
- 343
- Number
- 10
- Start Page
- 1
- End Page
- 18
- ISSN
- 0012-365X
- Abstract
- Lovasz (1965) characterized graphs without two vertex-disjoint cycles, which implies that such graphs have at most three vertices hitting all cycles. In this paper, we ask whether such a small hitting set exists for S-cycles, when a graph has no two vertex-disjoint S-cycles. For a graph G and a vertex set S of G, an S-cycle is a cycle containing a vertex of S.,We provide an example G on 21 vertices where G has no two vertex-disjoint S-cycles, but three vertices are not sufficient to hit all S-cycles. On the other hand, we show that four vertices are enough to hit all S-cycles whenever a graph has no two vertex-disjoint S-cycles. (C) 2020 Elsevier B.V. All rights reserved.,
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Related Researcher
- Kwon, O jung
- COLLEGE OF NATURAL SCIENCES (DEPARTMENT OF MATHEMATICS)