Year: 2024
Type: article
Abstract: For a set π of connected graphs, an π-factor is a spanning subgraph of a graph, whose connected components are isomorphic to graphs from the set π. An π-factor is also referred as a component factor. A graph G is called an (π, m)-factor deleted graph if for every Eβ² β E(G) with |Eβ²| = m, G β Eβ² admits an π-factor. A graph G is called an (π, l)-factor critical graph if for every Vβ² β V (G) with |Vβ²| = l, G β Vβ² admits an π-factor. Let m, l and k be three positive integers with k β₯ 2, and write β± = {P2, C3, P5, π― (3)} and β = {K1,1, K1,2, . . . , K1,k, π― (2k + 1)}, where π― (3) and π― (2k + 1) are two special families of trees. Inspired by finding a sufficient condition to check for the existence of path-factors with some special restraints, we focus on the sufficient conditions based on a graphic parameter called degree sum: ΟΞΊ(G) = minβ‘XβV(G) {Ξ£xβXdG(x):X is an independent set of k vertices}. In this article, we verify that: (i) an (l + 2)-connected graph G of order n is an (β±, l)-factor critical graph if Ο3(G) β₯ 6n+9l/5 ; (ii) a (2m + 1)-connected graph G of order n is an (β±, m)-factor deleted graph if Οm+2(G) β₯ 6/5n ; (iii) an (l + 2)-connected graph G of order n is an (β, l)-factor critical graph if Ο2k+1(G) β₯ 6n+(6k+3)l/2k+3 ; (iv) a (2m + 1)-connected graph G of order n is an (β, m)-factor deleted graph if Οm+2(G) β₯ 6n/2k+3 .
Source: RAIRO - Operations Research
DOI: 10.1051/ro/2024170
Authors: Hui Qin, Guowei Dai, Yuan Chen, Ting Jin, Yuan Yuan
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W4401687526