Discrete Mathematics

2003

DOI: 10.1016/s0012-365x(03)00289-9

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Maximum genus and chromatic number of graphs

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Some Lemmas2

Lemma 11 Every Loopless Graph Of Diameter Two Is Up-embedd1

Introduction1

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2007

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Cited by 6 publications

(4 citation statements)

References 14 publications

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“…The following result, which was proved by Huang [18] , provides a structural characterization for a non-upper embeddable graph.…”

Section: Some Lemmasmentioning

confidence: 93%

Up-embeddability via girth and the degree-sum of adjacent vertices

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2009

Sci. China Ser. A-Math.

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Let G be a simple graph of order n and girth g. For any two adjacent vertices u and vfor any two adjacent vertices u and v of G. Furthermore, the above three lower bounds are all shown to be tight.

“…The following result, which was proved by Huang [18] , provides a structural characterization for a non-upper embeddable graph.…”

Section: Some Lemmasmentioning

confidence: 93%

Up-embeddability via girth and the degree-sum of adjacent vertices

¹

,

²

2009

Sci. China Ser. A-Math.

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Let G be a simple graph of order n and girth g. For any two adjacent vertices u and vfor any two adjacent vertices u and v of G. Furthermore, the above three lower bounds are all shown to be tight.

“…The following lemma which is proved by Huang [17] plays a fundamental role throughout this paper. Lemma 1.9 [17] .…”

Section: Lemma 11 Every Loopless Graph Of Diameter Two Is Up-embeddmentioning

confidence: 96%

Results of the maximum genus of graphs

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²

2007

SCI CHINA SER A

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In this paper, we provide a new class of up-embeddable graphs, and obtain a tight lower bound on the maximum genus of a class of 2-connected pseudographs of diameter 2 and of a class of diameter 4 multi-graphs. This extends a result ofŠkoviera.

“…The following result due to Huang [8] provides a structural characterization for a non-upper embeddable graph, namely, the graph G with ξ(G) 2. [8] .…”

Section: Basic Lemmasmentioning

confidence: 99%

Upper embeddability, edge independence number and girth

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2009

Sci. China Ser. A-Math.

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Combined with the edge-connectivity, this paper investigates the relationship between the edge independence number and upper embeddability. And we obtain the following result:Let G be a k-edge-connected graph with girth g. Ifwhere k = 1, 2, 3, and α (G) denotes the edge independence number of G, then G is upper embeddable and the upper bound is best possible. And it has generalized the relative results.

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