H-packing of k-chromatic graphs

Raphael Yuster

H-packing of k-chromatic graphs

Department of Mathematics

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

Abstract

For graphs H and G, let Ph(G) denote the maximum number of edges covered by a set of edge-disjoint copies of H in G. We prove that if H is k-chromatic, then p_H(G) ≥≥pK_k(G) — o(|V(G)|²). The error term cannot be improved much, as for any δ > 0 there are graphs H with χ(H) = k such that for all n sufficiently large, there are graphs G with n vertices for which p_H(G) ≤ pK_k(G) — n^2-δ. We present several applications of this result in extremal graph theory.

Original language	English
Pages (from-to)	73-88
Number of pages	16
Journal	Moscow Journal of Combinatorics and Number Theory
Volume	2
Issue number	1
State	Published - 2012

Bibliographical note

Publisher Copyright:
© 2012, Mathematical Sciences Publishers. All rights reserved.

Keywords

H-packing
chromatic number
edge-packing

ASJC Scopus subject areas

Algebra and Number Theory
Discrete Mathematics and Combinatorics

Cite this

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abstract = "For graphs H and G, let Ph(G) denote the maximum number of edges covered by a set of edge-disjoint copies of H in G. We prove that if H is k-chromatic, then pH(G) ≥≥pKk(G) — o(|V(G)|2). The error term cannot be improved much, as for any δ > 0 there are graphs H with χ(H) = k such that for all n sufficiently large, there are graphs G with n vertices for which pH(G) ≤ pKk(G) — n2-δ. We present several applications of this result in extremal graph theory.",

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AB - For graphs H and G, let Ph(G) denote the maximum number of edges covered by a set of edge-disjoint copies of H in G. We prove that if H is k-chromatic, then pH(G) ≥≥pKk(G) — o(|V(G)|2). The error term cannot be improved much, as for any δ > 0 there are graphs H with χ(H) = k such that for all n sufficiently large, there are graphs G with n vertices for which pH(G) ≤ pKk(G) — n2-δ. We present several applications of this result in extremal graph theory.

KW - H-packing

KW - chromatic number

KW - edge-packing

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ER -

H-packing of k-chromatic graphs

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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