Abstract
A graph G is called fractional [a, b]-covered if for every \(e\in E(G)\), 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.
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The authors thank the referees for careful reading and some nice suggestions to improve the presentation of this paper.
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Lv, X. An improvement of the previous result on fractional (a,b,k)-critical covered graphs. Indian J Pure Appl Math 55, 40–46 (2024). https://doi.org/10.1007/s13226-022-00344-4
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DOI: https://doi.org/10.1007/s13226-022-00344-4
Keywords
- Graph
- Fan-type condition
- Fractional [a, b]-factor
- Fractional [a, b]-covered graph
- Fractional (a, b, k)-critical covered graph