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

Abstract

For two positive integers r and s with r ≥ 2s-2, if G is a graph of order 3r + 4s such that d(x) + d(y) ≥ 4r + 4s for every xy ⋯ E(G), then G independently contains r triangles and s quadrilaterals, which partially prove the El-Zahar's Conjecture.