Covering Graphs: The Covering Problem Solved

Yair Caro; Raphael Yuster

doi:10.1006/jcta.1998.2867

Covering Graphs: The Covering Problem Solved

Yair Caro, Raphael Yuster

Department of Mathematics

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

Abstract

For every fixed graphH, we determine theH-covering number ofK_n, for alln>n₀(H). We prove that ifhis the number of edges ofH, andgcd(H)=dis the greatest common divisor of the degrees ofH, then there existsn₀=n₀(H), such that for alln>n₀,C(H,K_n)=dn2hn-1d,unlessdis even,n=1 moddandn(n-1)/d+1=0 mod(2h/d), in which case[formula]Our main tool in proving this result is the deep decomposition result of Gustavsson.

Original language	English
Pages (from-to)	273-282
Number of pages	10
Journal	Journal of Combinatorial Theory. Series A
Volume	83
Issue number	2
DOIs	https://doi.org/10.1006/jcta.1998.2867
State	Published - Aug 1998

ASJC Scopus subject areas

Theoretical Computer Science
Discrete Mathematics and Combinatorics
Computational Theory and Mathematics

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10.1006/jcta.1998.2867

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title = "Covering Graphs: The Covering Problem Solved",

abstract = "For every fixed graphH, we determine theH-covering number ofKn, for alln>n0(H). We prove that ifhis the number of edges ofH, andgcd(H)=dis the greatest common divisor of the degrees ofH, then there existsn0=n0(H), such that for alln>n0,C(H,Kn)=dn2hn-1d,unlessdis even,n=1 moddandn(n-1)/d+1=0 mod(2h/d), in which case[formula]Our main tool in proving this result is the deep decomposition result of Gustavsson.",

author = "Yair Caro and Raphael Yuster",

year = "1998",

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doi = "10.1006/jcta.1998.2867",

language = "English",

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journal = "Journal of Combinatorial Theory. Series A",

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AB - For every fixed graphH, we determine theH-covering number ofKn, for alln>n0(H). We prove that ifhis the number of edges ofH, andgcd(H)=dis the greatest common divisor of the degrees ofH, then there existsn0=n0(H), such that for alln>n0,C(H,Kn)=dn2hn-1d,unlessdis even,n=1 moddandn(n-1)/d+1=0 mod(2h/d), in which case[formula]Our main tool in proving this result is the deep decomposition result of Gustavsson.

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Covering Graphs: The Covering Problem Solved

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