A degree sequence version of the K\"uhn-Osthus tiling theorem

TL;DR

This paper extends a key graph theory result by establishing a degree sequence condition that guarantees perfect H-tilings, even when many vertices have lower degrees, broadening the applicability of the original theorem.

Contribution

It introduces a degree sequence version of the K"uhn-Osthus tiling theorem, allowing for many vertices with lower degrees than previously permitted.

Findings

Proves a new degree sequence condition for perfect H-tilings.

Generalizes the original minimum degree threshold result.

Enhances understanding of graph packings with irregular degree distributions.

Abstract

A fundamental result of K\"uhn and Osthus [The minimum degree threshold for perfect graph packings, Combinatorica, 2009] determines up to an additive constant the minimum degree threshold that forces a graph to contain a perfect H-tiling. We prove a degree sequence version of this result which allows for a significant number of vertices to have lower degree.