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The maximum genus of a 3-regular simplicial graph

โœ Scribed by Li Deming; Liu Yanpei


Publisher
SP Editorial Committee of Applied Mathematics - A Journal of Chinese Universities
Year
1999
Tongue
English
Weight
601 KB
Volume
14
Category
Article
ISSN
1005-1031

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๐Ÿ“œ SIMILAR VOLUMES


Maximum genus and maximum nonseparating
โœ Yuangqiu Huang; Yanpei Liu ๐Ÿ“‚ Article ๐Ÿ“… 1997 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 440 KB

A set J C V is called a nonseparating independent set (nsis) of a connected graph G = (V, E), if J is an independent set of G, i.e., E A {uv [ Vu, v E J} = 0, and G -J is connected. We call z(G) = maxJ{lJ[ tJ is an nsis of G} the nsis number of G. Let G be a 3-regular connected graph; we prove that

A tight lower bound on the maximum genus
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It is proved that every connected simplicial graph with minimum valence at least three has maximum genus at least one-quarter of its cycle rank. This follows from the technical result that every 3-regular simplicial graph except K4 has a Xuong co-tree whose odd components have only one edge each. It

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