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Cyclic Degrees of 3-Polytopes

✍ Scribed by Oleg V. Borodin; Douglas R. Woodall

Book ID
106048030
Publisher
Springer Japan
Year
1999
Tongue
English
Weight
105 KB
Volume
15
Category
Article
ISSN
0911-0119

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πŸ“œ SIMILAR VOLUMES

Cyclic degree and cyclic coloring of 3-p
Cyclic degree and cyclic coloring of 3-polytopes
✍ Borodin, Oleg V. πŸ“‚ Article πŸ“… 1996 πŸ› John Wiley and Sons 🌐 English βš– 402 KB πŸ‘ 1 views

A vertex coloring of a plane graph is called cyclic if the vertices in each face bounding cycle are colored differently. The main result is an improvement of the upper bound for the cyclic chromatic number of 3-polytopes due to Plummer and Toft, 1987 (J. Graph Theory 11 (1 987) 505-51 7). The proof

Cyclic coloration of 3-polytopes
Cyclic coloration of 3-polytopes
✍ Michael D. Plummer; Bjarne Toft πŸ“‚ Article πŸ“… 1987 πŸ› John Wiley and Sons 🌐 English βš– 418 KB

A cyclic coloration of a planar graph G is an assignment of colors to the points of G such that for any face bounding cycle the points of f have different colors. We observe that the upper bound 2p\*(G), due to 0. Ore and M. D. Plummer, can be improved to p \* ( G ) + 9 when G is 3connected (p\* den

Almost cyclic polytopes
Almost cyclic polytopes
✍ Ido Shemer πŸ“‚ Article πŸ“… 1987 πŸ› Elsevier Science 🌐 English βš– 928 KB
Subpolytopes of Cyclic Polytopes
Subpolytopes of Cyclic Polytopes
✍ Tibor Bisztriczky; Gyula KΓ‘rolyi πŸ“‚ Article πŸ“… 2000 πŸ› Elsevier Science 🌐 English βš– 85 KB

A remarkable result of Shemer [7] states that the combinatorial structure of a neighbourly 2mpolytope determines the combinatorial structure of each of its subpolytopes. From this, it follows that every subpolytope of a cyclic 2m-polytope is cyclic. In this note, we present a direct proof of this co