Year: 2024
Type: article
Abstract: A spanning subgraph H of a graph G is called a path-factor if every component of H is a path. Wang and Zhang [RAIRO:RO 57 (2023) 2231–2237] conjectured that a connected graph G with δ(G) ≥ 5 contains a {P2, P5}-factor if δ(G)≥3α(G)−14, where δ(G) and α(G) denote the minimum degree and independence number of G, respectively. We show that the conjecture is true except G ≅ X ∨ 7K3, where X is a spanning subgraph of K3. Furthermore, we give two degree conditions for the existence of {P2, P5}-factors, one of which is a stronger version of Wang’s another conjecture. We also show the degree conditions are best possible.
Source: RAIRO - Operations Research
DOI: 10.1051/ro/2024184
Author: Ping Zhang
Institution: University of Shanghai for Science and Technology
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: diamond
Awards: G3641063112, G8318015284
OpenAlex ID: W4402698290