Channel Assignment with r-Dynamic Coloring

Zhu, Junlei; Bu, Yuehua

doi:10.1007/978-3-030-04618-7_4

Cited by 6 publications

(2 citation statements)

References 15 publications

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“…On the other hand, this structural theorem is applicable to an interesting problem the so-called list 3-dynamic coloring of graphs, which has many applications to the channel assignment problems, see [ZB18,ZB20]. For the continuity of this paper, we introduce the list 3-dynamic coloring in Section 3, where we give a sharp upper bound for the list 3-dynamic chromatic number of outer-1-planar graphs (see Theorem 8 in Section 3).…”

Section: Introductionmentioning

confidence: 99%

The structure and the list 3-dynamic coloring of outer-1-planar graphs

Li¹,

Zhang²

2021

Discrete Mathematics &Amp; Theoretical Computer Science

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An outer-1-planar graph is a graph admitting a drawing in the plane so that all vertices appear in the outer region of the drawing and every edge crosses at most one other edge. This paper establishes the local structure of outer-1-planar graphs by proving that each outer-1-planar graph contains one of the seventeen fixed configurations, and the list of those configurations is minimal in the sense that for each fixed configuration there exist outer-1-planar graphs containing this configuration that do not contain any of another sixteen configurations. There are two interesting applications of this structural theorem. First of all, we conclude that every (resp. maximal) outer-1-planar graph of minimum degree at least 2 has an edge with the sum of the degrees of its two end-vertices being at most 9 (resp. 7), and this upper bound is sharp. On the other hand, we show that the list 3-dynamic chromatic number of every outer-1-planar graph is at most 6, and this upper bound is best possible.

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Section: Introductionmentioning

confidence: 99%

The structure and the list 3-dynamic coloring of outer-1-planar graphs

Li¹,

Zhang²

2021

Discrete Mathematics &Amp; Theoretical Computer Science

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“…The aim of this paper is to improve those two results to a more detailed form, which not only confirms the existence of such a light edge but also shows in which configuration it is contained (see Theorem 4 in Section 2). Furthermore, this structural theorem is applicable to an interesting problem the so-called list 3-dynamic coloring of graphs, which has many applications to the channel assignment problems [42]. For the continuity of this paper, we will introduce the list 3-dynamic coloring in Section 3, where we give a sharp upper bound for the list 3-dynamic chromatic number of outer-1-planar graphs (see Theorem 8 in Section 3).…”

Section: Introductionmentioning

confidence: 99%

The structure and the list 3-dynamic coloring of outer-1-planar graphs

Li,

Zhang

2019

Preprint

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An outer-1-planar graph is a graph admitting a drawing in the plane for which all vertices belong to the outer face of the drawing and there is at most one crossing on each edge. This paper describes the local structure of outer-1-planar graphs by proving that each outer-1-planar graph contains one of the seventeen fixed configurations, and the list of those configurations is minimal in the sense that for each fixed configuration there exist outer-1-planar graphs containing this configuration that do not contain any of the other sixteen configurations. There are two interesting applications of this structural theorem.First of all, we conclude that every (resp. maximal) outer-1-planar graph with minimum degree at least 2 has an edge with the sum of the degrees of its two end-vertices being at most 9 (resp. 7), and this upper bound is sharp. On the other hand, we show that the list 3-dynamic chromatic number of every outer-1-planar graph is at most 6, and this upper bound is best possible.

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2-Distance $$(\varDelta +1)$$-Coloring of Sparse Graphs Using the Potential Method

Montassier

2021

Trends in Mathematics

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Channel Assignment with r-Dynamic Coloring

Cited by 6 publications

References 15 publications

The structure and the list 3-dynamic coloring of outer-1-planar graphs

The structure and the list 3-dynamic coloring of outer-1-planar graphs

The structure and the list 3-dynamic coloring of outer-1-planar graphs

2-Distance $$(\varDelta +1)$$-Coloring of Sparse Graphs Using the Potential Method

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