Path-factors involving paths of order seven and nine

Authors

Yoshimi Egawa, Tokyo University of ScienceFollow
Michitaka Furuya, Tokyo University of ScienceFollow

Publication Date

2016

Abstract

In this paper, we show the following two theorems (here c_i(G-Χ) is the number of components C of G-Χ with |V(C)|=i): (i) If a graph G satisfies c₁(G-Χ)+⅓c₃(G-Χ)+⅓c₅(G-Χ) ≤ ⅔ |Χ| for all Χ ≤ V(G), then G has a {Ρ₂},Ρ₇}-factor. (ii)If a graph G satisfies c₁}(G-Χ)+c₃}(G-Χ)+⅔ c₅}(G-Χ)+⅓c₇}(G-Χ) ≤ ⅔|Χ| for all Χ⊆ V(G), then G has a {P₂,P₉}-factor.

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 License.

Recommended Citation

Egawa, Yoshimi and Furuya, Michitaka (2016) "Path-factors involving paths of order seven and nine," Theory and Applications of Graphs: Vol. 3: Iss. 1, Article 5.
DOI: 10.20429/tag.2016.030105
Available at: https://digitalcommons.georgiasouthern.edu/tag/vol3/iss1/5