Geodesic
A degree condition for graphs being fractional (a, b, k)-critical covered
Filomat, Tome 37 (2023) no. 10, p. 3315

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DOI

A graph G is fractional [a, b]-covered if for any e ∈ E(G), G possesses a fractional [a, b]-factor including e. A graph G is fractional (a, b, k)-critical covered if G − Q is fractional [a, b]-covered for any Q ⊆ V(G) with |Q| = k. In this paper, we verify that a graph G of order n is fractional (a, b, k)-critical covered if n ≥ (a+b)((2r−3)a+b+r−2)+bk+2 b , δ(G) ≥ (r − 1)(a + 1) + k and max{d G (w 1), d G (w 2), · · · , d G (w r)} ≥ an + bk + 2 a + b for every independent vertex subset {w 1 , w 2 , · · · , w r } of G. Our main result is an improvement of the previous result [S. Zhou, Y. Xu, Z. Sun, Degree conditions for fractional (a, b, k)-critical covered graphs, Information Processing Letters 152(2019)105838].
DOI : 10.2298/FIL2310315L
Classification : 05C70, 90B99
Keywords: graph, degree condition, fractional (a, b, k)-critical covered graph 
Xiangyang Lv. A degree condition for graphs being fractional (a, b, k)-critical covered. Filomat, Tome 37 (2023) no. 10, p. 3315 . doi: 10.2298/FIL2310315L
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     author = {Xiangyang Lv},
     title = {A degree condition for graphs being fractional (a, b, k)-critical covered},
     journal = {Filomat},
     pages = {3315 },
     year = {2023},
     volume = {37},
     number = {10},
     doi = {10.2298/FIL2310315L},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/FIL2310315L/}
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