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A Degree Condition Implying Ore-Type Condition for Even [2,b]-Factors in Graphs

Shoichi Tsuchiya; Takamasa Yashima — 2017

Discussiones Mathematicae Graph Theory

For a graph G and even integers b ⩾ a ⩾ 2, a spanning subgraph F of G such that a ⩽ degF (x) ⩽ b and degF (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 degG (x),degG (y)⩾max 2n2+b,3 $max {{deg}_{G} (x), {deg}_{G} (y)} \geq max \{\frac{2 n}{2 + b}, 3\}$ for any nonadjacent vertices x and y of G. Moreover, we show that for b ⩾ 3a and a > 2, there exists an infinite family of 2-edge-connected graphs G of order n with δ(G) ⩾ a such that G...

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