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Tightening Nonsimple Paths and Cycles on Surfaces

✍ Scribed by de Verdière, Éric Colin; Erickson, Jeff

Book ID
118181090
Publisher
Society for Industrial and Applied Mathematics
Year
2010
Tongue
English
Weight
453 KB
Volume
39
Category
Article
ISSN
0097-5397

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📜 SIMILAR VOLUMES

On cycles and paths in digraphs
On cycles and paths in digraphs
✍ M.C. Heydemann 📂 Article 📅 1980 🏛 Elsevier Science 🌐 English ⚖ 273 KB

The purpose of this communication is to announce some slrfficient conditions on degrees and number of arcs to insure the existence of cycles and paths in directed graphs. We show that these results are the best possible. The proofs of the theorems can be found in [4].

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## Abstract For a graph __G__, __p__(__G__) and __c__(__G__) denote the order of a longest path and a longest cycle of __G__, respectively. In this paper, we prove that if __G__ is a 3 ‐connected graph of order __n__ such that the minimum degree sum of four independent vertices is at least __n__+ 6

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✍ Lai Yung-Ling; Kenneth Williams 📂 Article 📅 1997 🏛 Elsevier Science 🌐 English ⚖ 530 KB

The tensor product of graphs G1 and G2 is defined to be G= (V,E) where V = V(Gl ) x V(G2) and edge ((x~,.YI),(x~,Yz)) EE whenever (xI,xz)EE(GI) and (yl,yz)~E(G2). We use GI(Tp)G2 to denote G. This paper establishes the bandwidth of the tensor product of a path with a path, a cycle with a path, and