Remarks on path factors in graphs
RAIRO - Operations Research - Recherche Opérationnelle, Tome 54 (2020) no. 6, pp. 1827-1834.

A spanning subgraph of a graph is defined as a path factor of the graph if its component are paths. A P$$-factor means a path factor with each component having at least n vertices. A graph G is defined as a (P$$, m)-factor deleted graph if G–E′ has a P$$-factor for every E′ ⊆ E(G) with |E′| = m. A graph G is defined as a (P$$, k)-factor critical graph if after deleting any k vertices of G the remaining graph of G admits a P$$-factor. In this paper, we demonstrate that (i) a graph G is (P≥3, m)-factor deleted if κ(G) ≥ 2m + 1 and bind(G) ≥  2/3 - 3 2-1 4m+4; (ii) a graph G is (P≥3, k)-factor critical if κ(G) ≥ k + 2 and bind(G) ≥ 5+k 4.

DOI : 10.1051/ro/2019111
Classification : 05C70, 05C38, 90B10
Mots-clés : Graph, path factor, binding number, connectivity 
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     title = {Remarks on path factors in graphs},
     journal = {RAIRO - Operations Research - Recherche Op\'erationnelle},
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Zhou, Sizhong. Remarks on path factors in graphs. RAIRO - Operations Research - Recherche Opérationnelle, Tome 54 (2020) no. 6, pp. 1827-1834. doi : 10.1051/ro/2019111. http://www.numdam.org/articles/10.1051/ro/2019111/

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