On Degree Sum Conditions and Vertex-Disjoint Chorded Cycles

2019/11/20 by Bradley Elliott, Ronald J. Gould, Elliott, Bradley +3
Computer Science · Mathematics · #Advanced Graph Theory Research #Combinatorics (math.CO) #FOS: Mathematics #Graph theory and applications #Limits and Structures in Graph Theory

paper · pdf · doi:10.48550/arxiv.1911.08686

openalex publication_date 2019/11/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we consider a general degree sum condition sufficient to imply the existence of k vertex-disjoint chorded cycles in a graph G. Let σ_t(G) be the minimum degree sum of t independent vertices of G. We prove that if G is a graph of sufficiently large order and σ_t(G)≥ 3kt-t+1 with k≥ 1, then G contains k vertex-disjoint chorded cycles. We also show that the degree sum condition on σ_t(G) is sharp. To do this, we also investigate graphs without chorded cycles.

Citations

• On the maximal number of independent circuits in a graph

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