On the lower bounds for the maximum genus for simple graphs

Ouyang, Zhangdong; Wang, Jing; Huang, Yuanqiu

doi:10.1016/j.ejc.2009.11.001

Cited by 4 publications

(3 citation statements)

References 11 publications

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“…Furthermore, there are examples shown that the bound may be tight, and, in some sense, may be better than the result obtained by Li and Liu [8] , and the result obtained by Z. Ouyang etc. [9] .…”

Section: Lower Bound On the Maximum Genus Of Graphsmentioning

confidence: 99%

“…Ten years later, Z. Ouyang, J. Wang and Y. Huang [9] studied this parameter too, and obtained that: Let G be a k-edge-connected (or k-connected) simple graph with minimum degree δ and girth g.…”

Section: Subcase 12mentioning

confidence: 99%

“…Furthermore, it may be better than the result obtained by Li and Liu [8] and the result of Z. Ouyang etc. [9] . The following are two examples with girth 3 and connectivity 2, and girth 4 and connectivity 3 respectively.…”

Section: ⌉+3mentioning

confidence: 99%

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The extremal genus embedding of graphs

Dong,

Ren,

Wang

et al. 2012

Preprint

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Let W n be a wheel graph with n spokes. How does the genus change if adding a degree-3 vertex v, which is not in V (W n ), to the graph W n ? In this paper, through the joint-tree model we obtain that the genus of W n +v equals 0 if the three neighbors of v are in the same face boundary of P(W n ); otherwise, γ(W n +v) = 1, where P(W n ) is the unique planar embedding of W n . In addition, via the independent set, we provide a lower bound on the maximum genus of graphs, which may be better than both the result of D. Li & Y. Liu and the result of Z. Ouyang etc. in Europ. J. Combinatorics. Furthermore, we obtain a relation between the independence number and the maximum genus of graphs, and provide an algorithm to obtain the lower bound on the number of the distinct maximum genus embedding of the complete graph K m , which, in some sense, improves the result of Y. Caro and S. Stahl respectively.

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Section: Lower Bound On the Maximum Genus Of Graphsmentioning

confidence: 99%

Section: Subcase 12mentioning

confidence: 99%