An improvement of the previous result on fractional (a,b,k)-critical covered graphs

Xiangyang Lv ()
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Xiangyang Lv: Jiangsu University of Science and Technology

Indian Journal of Pure and Applied Mathematics, 2024, vol. 55, issue 1, 40-46

Abstract: Abstract A graph G is called fractional [a, b]-covered if for every $$e\in E(G)$$ e ∈ E ( G ) , G has a fractional [a, b]-factor containing e. A graph G is called fractional (a, b, k)-critical covered if after deleting any k vertices of G, the remaining graph of G is fractional [a, b]-covered. In this paper, we pose a Fan-type condition for a graph being fractional (a, b, k)-critical covered, which is an improvement of Zhou, Xu and Sun’s previous result [S. Zhou, Y. Xu, Z. Sun, Degree conditions for fractional (a, b, k)-critical covered graphs, Information Processing Letters 152(2019)105838]. Furthermore, we claim that the main result in this paper is best possible in some sense.

Keywords: Graph; Fan-type condition; Fractional [a; b]-factor; Fractional [a; b]-covered graph; Fractional (a; b; k)-critical covered graph; 05C70; 90B99 (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s13226-022-00344-4

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