Packing minor-closed families of graphs into complete graphs

TL;DR

This paper generalizes a recent result on packing collections of trees into complete graphs to broader classes of graphs within any non-trivial minor-closed class, expanding the scope of graph packing theory.

Contribution

It extends the packing results from trees to arbitrary graphs in any non-trivial minor-closed class, relaxing previous restrictions.

Findings

Successfully generalized packing results to broader graph classes.

Established conditions under which graphs in minor-closed classes can be packed.

Enhanced understanding of graph packing possibilities within complex graph families.

Abstract

Motivated by a conjecture of Gy\'arf\'as, recently B\"ottcher, Hladk\'y, Piguet, and Taraz showed that every collection $T_1,\dots,T_t$ of trees on $n$ vertices with $\sum_{i=1}^te(T_i)\leq \binom{n}{2}$ and with bounded maximum degree, can be packed into the complete graph on $(1+o(1))n$ vertices. We generalise this result where we relax the restriction of packing families of trees to families of graphs of any given non-trivial minor-closed class of graphs.