Existence of all generalized fractional <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" id="d1e101" altimg="si31.svg"><mml:mrow><mml:mo>(</mml:mo><mml:mi>g</mml:mi><mml:mo>,</mml:mo><mml:mi>f</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math>-factors of graphs

Egawa, Yoshimi; Kanō, Mikio; Yokota, Maho

doi:10.1016/j.dam.2020.01.014

Cited by 7 publications

(1 citation statement)

References 3 publications

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“…In the past decades, some researchers provided various parameter conditions for a graph to have an [a, b]-factor, such as the degree condition [28], the neighborhood condition [25], the stability number [17], and the binding number [7]. In addition, the conditions for a graph to have a fractional [a, b]-factor (see [34] for the definition) was also investigated by several researchers [11,18,21]. Only very recently, Cho, Hyun, O and Park [6] posed a conjecture regarding the spectral condition for the existence of an [a, b]-factor as follows.…”

Section: Introductionmentioning

confidence: 99%

Spectral radius and $[a,b]$-factors in graphs

Ding¹,

Lin²,

Lu³

2021

Preprint

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An [a, b]-factor of a graph G is a spanning subgraph H such that a ≤ d H (v) ≤ b for each v ∈ V (G). In this paper, we provide spectral conditions for the existence of an odd [1, b]-factor in a connected graph with minimum degree δ and the existence of an [a, b]-factor in a graph, respectively. Our results generalize and improve some previous results on perfect matchings of graphs. For a = 1, we extend the result of O [30] to obtain an odd [1, b]-factor and further improve the result of Liu, Liu and Feng [27] for a = b = 1. For n ≥ 3a + b − 1, we confirm the conjecture of Cho, Hyun, O and Park [6]. We conclude some open problems in the end.

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Section: Introductionmentioning

confidence: 99%

Spectral radius and $[a,b]$-factors in graphs

Ding¹,

Lin²,

Lu³

2021

Preprint

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Fuzzy fractional factors in fuzzy graphs

Gao

Wang

Zheng

2022

Int J of Intelligent Sys

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Graph fractional factor theory plays a crucial role in data transmission and network flow existence analysis, and has become one of the hot research branches of graph theory. This paper introduces fuzzy fractional factor in fuzzy graph setting, and an algorithm-based proof of its necessary and sufficient condition is given. The transformation operation is introduced to show that any two fuzzy fractional f -factors can be converted between each other, and the characteristic of maximum fuzzy fractional factor through increasing walk is determined. Finally, toughness in fuzzy graph setting is introduced, and preliminary toughness bound for fuzzy fractional ι-factor is presented, where ι μ e μ e = min { ( ) ( ) > 0}

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A note on fractional ID-[a,b]-factor-critical covered graphs

Zhou

Liu

2022

Discrete Applied Mathematics

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Existence of all generalized fractional (g,f)-factors of graphs

Cited by 7 publications

References 3 publications

Spectral radius and $[a,b]$-factors in graphs

Spectral radius and $[a,b]$-factors in graphs

Fuzzy fractional factors in fuzzy graphs

A note on fractional ID-[a,b]-factor-critical covered graphs

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