In this paper, we prove that any graph G with maximum degree รG ! 11 p 49ร241AEa2, which is embeddable in a surface AE of characteristic 1AE 1 and satisยฎes jVGj b 2รGร5ร2 p 6รG, is class one.
3-Coloring graphs embedded in surfaces
โ Scribed by Zhao, Yue
- Publisher
- John Wiley and Sons
- Year
- 2000
- Tongue
- English
- Weight
- 66 KB
- Volume
- 33
- Category
- Article
- ISSN
- 0364-9024
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โฆ Synopsis
In this article, we show that there exists an integer k(ฮฃ)
๐ SIMILAR VOLUMES
Fix any positive integer n. Let S be the set of all Steinhaus graphs of order n(n -1)/2 + 1. The vertices for each graph in S are the first n(n -1)/2 + 1 positive integers. Let I be the set of all labeled graphs of order n with vertices of the form i(i -1)/2 + 1 for the first n positive integers i.
A well-known Tutte's theorem claims that every 3-connected planar graph has a convex embedding into the plane. Tutte's arguments also show that, moreover, for every nonseparating cycle C of a 3-connected graph G, there exists a convex embedding of G such that C is a boundary of the outer face in thi
For the bandwidth B(G) and the cyclic bandwidth B c (G) of a graph G, it is known that 1 2 B(G) ยฐBc (G) ยฐB(G). In this paper, the criterion conditions for two extreme cases B c (G) ร B(G) and B c (G) ร 1 2 B(G) are studied. From this, some exact values of B c (G) for special graphs can be obtained.