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

Shoichi Tsuchiya; Takamasa Yashima

Discussiones Mathematicae Graph Theory (2017)

- Volume: 37, Issue: 3, page 797-809
- ISSN: 2083-5892

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topShoichi Tsuchiya, and Takamasa Yashima. "A Degree Condition Implying Ore-Type Condition for Even [2,b]-Factors in Graphs." Discussiones Mathematicae Graph Theory 37.3 (2017): 797-809. <http://eudml.org/doc/288445>.

@article{ShoichiTsuchiya2017,

abstract = {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 \lbrace \deg _G (x),\deg _G (y)\rbrace \ge \max \left\lbrace \{\{\{2n\} \over \{2 + b\}\},3\} \right\rbrace $ 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 satisfies the condition [...] degG (x)+degG (y)>2ana+b $\deg _G (x) + \deg _G (y) > \{\{2an\} \over \{a + b\}\}$ 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.},

author = {Shoichi Tsuchiya, Takamasa Yashima},

journal = {Discussiones Mathematicae Graph Theory},

keywords = {[a,b]-factor; even factor; 2-edge-connected; minimum degree},

language = {eng},

number = {3},

pages = {797-809},

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

url = {http://eudml.org/doc/288445},

volume = {37},

year = {2017},

}

TY - JOUR

AU - Shoichi Tsuchiya

AU - Takamasa Yashima

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

JO - Discussiones Mathematicae Graph Theory

PY - 2017

VL - 37

IS - 3

SP - 797

EP - 809

AB - 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 \lbrace \deg _G (x),\deg _G (y)\rbrace \ge \max \left\lbrace {{{2n} \over {2 + b}},3} \right\rbrace $ 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 satisfies the condition [...] degG (x)+degG (y)>2ana+b $\deg _G (x) + \deg _G (y) > {{2an} \over {a + b}}$ 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.

LA - eng

KW - [a,b]-factor; even factor; 2-edge-connected; minimum degree

UR - http://eudml.org/doc/288445

ER -

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