Degree conditions for the partition of a graph into triangles and quadrilaterals

Details Degree conditions for the partition of a graph into triangles and quadrilaterals Degree conditions for the partition of a graph into triangles and quadrilaterals

2010-12-29

arxiv.org/abs/1012.5920v2

Utilitas Mathmatica 86 (2011) 341-346

Mathematics

Combinatorics

Scientific paper

For two positive integers $r$ and $s$ with $r\geq 2s-2$, if $G$ is a graph of
order $3r+4s$ such that $d(x)+d(y)\geq 4r+4s$ for every $xy\not\in E(G)$, then
$G$ independently contains $r$ triangles and $s$ quadrilaterals, which
partially prove the El-Zahar's Conjecture.

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