Path-factors involving paths of order seven and nine

2015/07/25 by Yoshimi Egawa, Egawa, Yoshimi, Michitaka Furuya +1
Computer Science · Engineering · Mathematics · #05C70 #Combinatorics (math.CO) #FOS: Mathematics #Graph Labeling and Dimension Problems #Limits and Structures in Graph Theory #graph theory and CDMA systems #math.CO #msc:05C70

paper · pdf · doi:10.48550/arxiv.1507.07066

29 pages, 4 figures

arxiv created 2015/07/25 · openalex publication_date 2015/07/25 · arxiv updated 2015/07/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we show the following two theorems (here c_i(G-X) is the number of components C of G-X with |V(C)|=i): (i)~If a graph G satisfies c₁(G-X)+(1)/(3)c₃(G-X)+(1)/(3)c₅(G-X)≤ (2)/(3)|X| for all X⊆ V(G), then G has a \P₂,P₇\-factor. (ii)~If a graph G satisfies c₁(G-X)+c₃(G-X)+(2)/(3)c₅(G-X)+(1)/(3)c₇(G-X)≤ (2)/(3)|X| for all X⊆ V(G), then G has a \P₂,P₉\-factor.

Citations

• The existence of a path-factor without small odd paths

Related

• The existence of a path-factor without small odd paths
• Sufficient conditions for the existence of a path-factor which are related to odd components
• Sufficient conditions for the existence of path-factors with given properties
• Some sufficient conditions for path-factor uniform graphs
• An Alternative Proof of the H-Factor Theorem