Decomposing edge-colored graphs under color degree constraints

Fujita, Shinya; Li, Ruonan; Wang, Guanghui

doi:10.1016/j.endm.2017.06.078

Cited by 6 publications

(5 citation statements)

References 13 publications

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“…Furthermore, the bound is best possible. Besides, Yeo's theorem is frequently used not only on the existence of PC cycles (see the survey paper [1] and recent results [8,13,17,19]) but also on other topics, such as PC trees [7], decomposition of edge-colored graphs [12],…”

Section: Introductionmentioning

confidence: 99%

A revisit to Bang-Jensen-Gutin conjecture and Yeo's theorem

Li¹,

Niu²

2022

Preprint

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A path (cycle) is properly-colored if consecutive edges are of distinct colors. In 1997, Bang-Jensen and Gutin conjectured a necessary and sufficient condition for the existence of a Hamilton path in an edge-colored complete graph. This conjecture, confirmed by Feng, Giesen, Guo, Gutin, Jensen and Rafley in 2006, was laterly playing an important role in Lo's asymptotical proof of Bollobás-Erdős' conjecture on properly-colored Hamilton cycles. In 1997, Yeo obtained a structural characterization of edge-colored graphs that containing no properly colored cycles. This result is a fundamental tool in the study of edge-colored graphs. In this paper, we first give a much shorter proof of the Bang-Jensen-Gutin Conjecture by two novel absorbing lemmas. We also prove a new sufficient condition for the existence of a properly-colored cycle and then deduce Yeo's theorem from this result and a closure concept in edge-colored graphs.

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Section: Introductionmentioning

confidence: 99%

A revisit to Bang-Jensen-Gutin conjecture and Yeo's theorem

Li¹,

Niu²

2022

Preprint

Self Cite

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“…For related problems on graph partitioning under degree constraints or other variances, we refer readers to [2,3,5,10,13,14]. In this paper, we consider partitions of graphs and give a unified generalization of Theorems 2, 3 and 4 as well as the result of Diwan [4].…”

Section: Introductionmentioning

confidence: 99%

A Generalization of Stiebitz-Type Results on Graph Decomposition

Zeng

2021

Electron. J. Combin.

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In this paper, we consider the decomposition of multigraphs under minimum degree constraints and give a unified generalization of several results by various researchers. Let $G$ be a multigraph in which no quadrilaterals share edges with triangles and other quadrilaterals and let $\mu_G(v)=\max\{\mu_G(u,v):u\in V(G)\setminus\{v\}\}$, where $\mu_G(u,v)$ is the number of edges joining $u$ and $v$ in $G$. We show that for any two functions $a,b:V(G)\rightarrow\mathbb{N}\setminus\{0,1\}$, if $d_G(v)\ge a(v)+b(v)+2\mu_G(v)-3$ for each $v\in V(G)$, then there is a partition $(X,Y)$ of $V(G)$ such that $d_X(x)\geq a(x)$ for each $x\in X$ and $d_Y(y)\geq b(y)$ for each $y\in Y$. This extends the related results due to Diwan, Liu–Xu and Ma–Yang on simple graphs to the multigraph setting.

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“…For related problems on graph partitioning under degree constraints or other variances, we refer readers to [2,4,9,12,13]. In this paper, we consider the partitions of graphs and give a unified generalization of Theorems 1.2, 1.3 and 1.4 as well as the result of Diwan [3].…”

Section: Introductionmentioning

confidence: 99%

A generalization of Stiebitz-type results on graph decomposition

Zeng

Zu²

2020

Preprint

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In this paper, we consider the decomposition of multigraphs under minimum degree constraints and give a unified generalization of several results by various researchers. Let G be a multigraph in which no quadrilaterals share edges with triangles and other quadrilaterals and let µis the number of edges joining u and v in G. We show that for any two functions a, b :for each x ∈ X and d Y (y) ≥ b(y) for each y ∈ Y . This extends the related results due to Diwan [3], Liu and Xu [7] and Ma and Yang [10] on simple graphs to the multigraph setting.

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Decomposing edge-colored graphs under color degree constraints

Cited by 6 publications

References 13 publications

A revisit to Bang-Jensen-Gutin conjecture and Yeo's theorem

A revisit to Bang-Jensen-Gutin conjecture and Yeo's theorem

A Generalization of Stiebitz-Type Results on Graph Decomposition

A generalization of Stiebitz-type results on graph decomposition

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