### Abstract

Given graphs H_{1}, . . . , H_{k}, let f(H_{1}, . . . , H_{k}) be the minimum order of a graph G such that for each i, the induced copies of H_{i} in G cover V(G) We prove constructively that f(H_{1}, H_{2}) ≤ 2(n(H_{1}) + n(H_{2}) - 2); equality holds when H_{1} = H̄_{2} = K_{n}. We prove that f(H_{1},K̄_{n}) = n + 2√δ(H_{1})n + O(1) as n → ∞. We also determine f(K_{1,m - 1},K̄_{n}) exactly.

Original language | English |
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Pages (from-to) | 180-190 |

Number of pages | 11 |

Journal | Journal of Graph Theory |

Volume | 34 |

Issue number | 2 |

Publication status | Published - Jun 2000 |

### Fingerprint

### Keywords

- Framing number
- Induced subgraph
- Vertex covering

### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

*Journal of Graph Theory*,

*34*(2), 180-190.

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

Research output: Contribution to journal › Article

*Journal of Graph Theory*, vol. 34, no. 2, pp. 180-190.

}

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 -