Geodesic
A Degree Condition Implying Ore-Type Condition for Even [2, b]-Factors in Graphs
Discussiones Mathematicae. Graph Theory, Tome 37 (2017) no. 3, pp. 797-809.

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For a graph G and even integers b ≥ a ≥ 2, a spanning subgraph F of G such that a ≤deg_F (x) ≤ b and deg_F (x) is even for all x ∈ V (F) is called an even [a, b]-factor of G. In this paper, we show that a 2-edge-connected graph G of order n has an even [2, b]-factor if max{deg_G (x) , deg_G (y) }≥max{2n/2+b , 3 } for any nonadjacent vertices x and y of G. Moreover, we show that for b ≥ 3a and a gt; 2, there exists an infinite family of 2-edge-connected graphs G of order n with δ (G) ≥ a such that G satisfies the condition deg_G (x) + deg_G (y) gt; 2an/a+b for any nonadjacent vertices x and y of G, but has no even [a, b]-factors. In particular, the infinite family of graphs gives a counterexample to the conjecture of Matsuda on the existence of an even [a, b]-factor.
Keywords: [ a, b ]-factor, even factor, 2-edge-connected, minimum degree 
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Tsuchiya, Shoichi; Yashima, Takamasa. A Degree Condition Implying Ore-Type Condition for Even [2, b]-Factors in Graphs. Discussiones Mathematicae. Graph Theory, Tome 37 (2017) no. 3, pp. 797-809. http://geodesic.mathdoc.fr/item/DMGT_2017_37_3_a20/

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