Packing graphs: The packing problem solved

Yair Caro; Raphael Yuster

Packing graphs: The packing problem solved

Department of Mathematics

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

Abstract

For every fixed graph H, we determine the H-packing number of K_n, for all n > n₀(H). We prove that if h is the number of edges of H, and gcd(H) = d is the greatest common divisor of the degrees of H, then there exists n₀ = n₀(H), such that for all n > n₀, P(H, K_n) = ⌊dn/2h⌊n - 1/d⌋⌋, unless n = 1 mod d and n(n - 1)/d = b mod (2n/d) where 1 ≤ 6 ≤ d, in which case P(H, K_n) = ⌊dn/2h⌊n - 1/d⌋⌋ - 1. Our main tool in proving this result is the deep decomposition result of Gustavsson.

Original language	English
Article number	R1
Pages (from-to)	1-7
Number of pages	7
Journal	Electronic Journal of Combinatorics
Volume	4
Issue number	1
State	Published - 1997

ASJC Scopus subject areas

Theoretical Computer Science
Geometry and Topology
Discrete Mathematics and Combinatorics
Computational Theory and Mathematics
Applied Mathematics

Cite this

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title = "Packing graphs: The packing problem solved",

abstract = "For every fixed graph H, we determine the H-packing number of Kn, for all n > n0(H). We prove that if h is the number of edges of H, and gcd(H) = d is the greatest common divisor of the degrees of H, then there exists n0 = n0(H), such that for all n > n0, P(H, Kn) = ⌊dn/2h⌊n - 1/d⌋⌋, unless n = 1 mod d and n(n - 1)/d = b mod (2n/d) where 1 ≤ 6 ≤ d, in which case P(H, Kn) = ⌊dn/2h⌊n - 1/d⌋⌋ - 1. Our main tool in proving this result is the deep decomposition result of Gustavsson.",

author = "Yair Caro and Raphael Yuster",

year = "1997",

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T1 - Packing graphs

T2 - The packing problem solved

AU - Caro, Yair

AU - Yuster, Raphael

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N2 - For every fixed graph H, we determine the H-packing number of Kn, for all n > n0(H). We prove that if h is the number of edges of H, and gcd(H) = d is the greatest common divisor of the degrees of H, then there exists n0 = n0(H), such that for all n > n0, P(H, Kn) = ⌊dn/2h⌊n - 1/d⌋⌋, unless n = 1 mod d and n(n - 1)/d = b mod (2n/d) where 1 ≤ 6 ≤ d, in which case P(H, Kn) = ⌊dn/2h⌊n - 1/d⌋⌋ - 1. Our main tool in proving this result is the deep decomposition result of Gustavsson.

AB - For every fixed graph H, we determine the H-packing number of Kn, for all n > n0(H). We prove that if h is the number of edges of H, and gcd(H) = d is the greatest common divisor of the degrees of H, then there exists n0 = n0(H), such that for all n > n0, P(H, Kn) = ⌊dn/2h⌊n - 1/d⌋⌋, unless n = 1 mod d and n(n - 1)/d = b mod (2n/d) where 1 ≤ 6 ≤ d, in which case P(H, Kn) = ⌊dn/2h⌊n - 1/d⌋⌋ - 1. Our main tool in proving this result is the deep decomposition result of Gustavsson.

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JF - Electronic Journal of Combinatorics

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Packing graphs: The packing problem solved

Abstract

ASJC Scopus subject areas

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