Multiple vertex coverings by specified induced subgraphs

Z. Füredi, Dhruv Mubayi, Douglas B. West

Research output: Contribution to journalArticle

3 Citations (Scopus)

Abstract

Given graphs H1, . . . , Hk, let f(H1, . . . , Hk) be the minimum order of a graph G such that for each i, the induced copies of Hi in G cover V(G) We prove constructively that f(H1, H2) ≤ 2(n(H1) + n(H2) - 2); equality holds when H1 = H̄2 = Kn. We prove that f(H1,K̄n) = n + 2√δ(H1)n + O(1) as n → ∞. We also determine f(K1,m - 1,K̄n) exactly.

Original languageEnglish
Pages (from-to)180-190
Number of pages11
JournalJournal of Graph Theory
Volume34
Issue number2
Publication statusPublished - Jun 2000

Fingerprint

Induced Subgraph
Covering
Graph in graph theory
Vertex of a graph
Equality
Cover

Keywords

  • Framing number
  • Induced subgraph
  • Vertex covering

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Multiple vertex coverings by specified induced subgraphs. / Füredi, Z.; Mubayi, Dhruv; West, Douglas B.

In: Journal of Graph Theory, Vol. 34, No. 2, 06.2000, p. 180-190.

Research output: Contribution to journalArticle

Füredi, Z, Mubayi, D & West, DB 2000, 'Multiple vertex coverings by specified induced subgraphs', Journal of Graph Theory, vol. 34, no. 2, pp. 180-190.
Füredi, Z. ; Mubayi, Dhruv ; West, Douglas B. / Multiple vertex coverings by specified induced subgraphs. In: Journal of Graph Theory. 2000 ; Vol. 34, No. 2. pp. 180-190.
@article{40703a2550f54c1c8b665827e148f5d7,
title = "Multiple vertex coverings by specified induced subgraphs",
abstract = "Given graphs H1, . . . , Hk, let f(H1, . . . , Hk) be the minimum order of a graph G such that for each i, the induced copies of Hi in G cover V(G) We prove constructively that f(H1, H2) ≤ 2(n(H1) + n(H2) - 2); equality holds when H1 = H̄2 = Kn. We prove that f(H1,K̄n) = n + 2√δ(H1)n + O(1) as n → ∞. We also determine f(K1,m - 1,K̄n) exactly.",
keywords = "Framing number, Induced subgraph, Vertex covering",
author = "Z. F{\"u}redi and Dhruv Mubayi and West, {Douglas B.}",
year = "2000",
month = "6",
language = "English",
volume = "34",
pages = "180--190",
journal = "Journal of Graph Theory",
issn = "0364-9024",
publisher = "Wiley-Liss Inc.",
number = "2",

}

TY - JOUR

T1 - Multiple vertex coverings by specified induced subgraphs

AU - Füredi, Z.

AU - Mubayi, Dhruv

AU - West, Douglas B.

PY - 2000/6

Y1 - 2000/6

N2 - Given graphs H1, . . . , Hk, let f(H1, . . . , Hk) be the minimum order of a graph G such that for each i, the induced copies of Hi in G cover V(G) We prove constructively that f(H1, H2) ≤ 2(n(H1) + n(H2) - 2); equality holds when H1 = H̄2 = Kn. We prove that f(H1,K̄n) = n + 2√δ(H1)n + O(1) as n → ∞. We also determine f(K1,m - 1,K̄n) exactly.

AB - Given graphs H1, . . . , Hk, let f(H1, . . . , Hk) be the minimum order of a graph G such that for each i, the induced copies of Hi in G cover V(G) We prove constructively that f(H1, H2) ≤ 2(n(H1) + n(H2) - 2); equality holds when H1 = H̄2 = Kn. We prove that f(H1,K̄n) = n + 2√δ(H1)n + O(1) as n → ∞. We also determine f(K1,m - 1,K̄n) exactly.

KW - Framing number

KW - Induced subgraph

KW - Vertex covering

UR - http://www.scopus.com/inward/record.url?scp=0034197820&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0034197820&partnerID=8YFLogxK

M3 - Article

VL - 34

SP - 180

EP - 190

JO - Journal of Graph Theory

JF - Journal of Graph Theory

SN - 0364-9024

IS - 2

ER -