H-packing of k-chromatic graphs

Raphael Yuster

H-packing of k-chromatic graphs

Raphael Yuster

Department of Mathematics

University of Haifa

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	American 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

Keywords

chromatic number
edge-packing
H-packing

All Science Journal Classification (ASJC) codes

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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N2 - 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.

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 - chromatic number

KW - edge-packing

KW - H-packing

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M3 - Article

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VL - 2

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JO - Moscow Journal of Combinatorics and Number Theory

JF - Moscow Journal of Combinatorics and Number Theory

IS - 1

ER -

H-packing of k-chromatic graphs

Abstract

Keywords

All Science Journal Classification (ASJC) codes

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