Packing Graphs: The Packing Problem Solved

Author:

Caro Yair,Yuster Raphael

Abstract

For every fixed graph $H$, we determine the $H$-packing number of $K_n$, for all $n > n_0(H)$. 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 $n_0=n_0(H)$, such that for all $n > n_0$, $$ P(H,K_n)=\lfloor {{dn}\over{2h}} \lfloor {{n-1}\over{d}} \rfloor \rfloor, $$ unless $n = 1 \bmod d$ and $n(n-1)/d = b \bmod (2h/d)$ where $1 \leq b \leq d$, in which case $$ P(H,K_n)=\lfloor {{dn}\over{2h}} \lfloor {{n-1}\over{d}} \rfloor \rfloor - 1. $$ Our main tool in proving this result is the deep decomposition result of Gustavsson.

Publisher

The Electronic Journal of Combinatorics

Subject

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

Cited by 10 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. Packing cliques in 3‐uniform hypergraphs;Journal of Combinatorial Designs;2020-04-22

2. Generalising Fisher’s inequality to coverings and packings;Combinatorica;2016-10-17

3. An approximate version of the tree packing conjecture;Israel Journal of Mathematics;2016-01-05

4. Covering and packing for pairs;Journal of Combinatorial Theory, Series A;2013-09

5. Planar Packing of Binary Trees;Lecture Notes in Computer Science;2013

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