On the Existence of Disjoint Cycles in a Graph

Abstract

A simple proof of the following result is given: Suppose G is a graph of order at least 3k with σ 2 (G) ≥ 4k − 1. Then G contains k vertex-disjoint cycles.

Graphs Containing Every 2-Factor

“…Justesen [11] proved an Ore-type version of the Corrádi-Hajnal Theorem by showing that every n-vertex graph G with σ 2 (G) ≥ 4n/3 contains ⌊n/3⌋ disjoint triangles. Enomoto [9], and Wang [18] sharpened this result. In particular, they proved the following.…”

“…So, e G ({y ′ 1 , y ′ 2 }, {w 2 , w 3 , w 4 }) ≥ 4. By (9), w 1 has a neighbor in {y ′ 1 , y ′ 2 }. By symmetry, we may assume that y ′ 1 w 1 ∈ E(G).…”

Sufficient Condition for the Existence of Three Disjoint Theta Graphs

“…Later, Wang [10] and independently Enomoto [5] proved a result stronger than Theorem 1.1 as follows.…”

An Ore-type analogue of the Sauer-Spencer Theorem

“…Several Ore-type results on packing appear in [5,8,11]. The goal of this note is to prove an Ore-type analogue of Theorems 1 and 2.…”