𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Cyclic coloring of plane graphs

✍ Scribed by Oleg V. Borodin

Publisher
Elsevier Science
Year
1992
Tongue
English
Weight
637 KB
Volume
100
Category
Article
ISSN
0012-365X

No coin nor oath required. For personal study only.

✦ Synopsis

Borodin, O.V., Cyclic coloring of plane graphs, Discrete Mathematics 100 (1992) 281-289. Let G be a plane graph, and let x,(G) be the minimum number of colors to color the vertices of G so that every two of them which lie in the boundary of the same face of the size at most k, receive different colors. In 1966, Ore and Plummer proved that x,(G) s 2k for any k 3 3. It is also known that x3(G) 6 4 (Appel and Haken, 1976) and x4(G) c 6 (Borodin, 1984). The result in the present paper is: q(G) c 9, x6(G) s 11, X,(G) s 12, and+(G) ~2k -3 if k 2 8.

📜 SIMILAR VOLUMES

Coloring plane graphs with independent c
Coloring plane graphs with independent crossings
✍ Daniel Král'; Ladislav Stacho 📂 Article 📅 2009 🏛 John Wiley and Sons 🌐 English ⚖ 268 KB

## Abstract We show that every plane graph with maximum face size four in which all faces of size four are vertex‐disjoint is cyclically 5‐colorable. This answers a question of Albertson whether graphs drawn in the plane with all crossings independent are 5‐colorable. © 2009 Wiley Periodicals, Inc.

Facial non-repetitive edge-coloring of p
Facial non-repetitive edge-coloring of plane graphs
✍ Frédéric Havet; Stanislav Jendrol'; Roman Soták; Erika Škrabul'áková 📂 Article 📅 2010 🏛 John Wiley and Sons 🌐 English ⚖ 124 KB

A sequence r 1 , r 2 , . . . , r 2n such that r i = r n+i for all 1 ≤ i ≤ n is called a repetition. A sequence S is called non-repetitive if no block (i.e. subsequence of consecutive terms of S) is a repetition. Let G be a graph whose edges are colored. A trail is called non-repetitive if the sequen

Simultaneous coloring of edges and faces
Simultaneous coloring of edges and faces of plane graphs
✍ Oleg V. Borodin 📂 Article 📅 1994 🏛 Elsevier Science 🌐 English ⚖ 888 KB

The edges and faces of a plane graph are colored so that every two adjacent or incident of them are colored differently. The minimal number of colors for this kind of coloring is estimated. For the plane graphs of the maximal degree at least 10, the bound is the best possible. The proof is based on

Edge-face coloring of plane graphs with
Edge-face coloring of plane graphs with maximum degree nine
✍ Jean-Sébastien Sereni; Matěj Stehlík 📂 Article 📅 2010 🏛 John Wiley and Sons 🌐 English ⚖ 189 KB 👁 1 views

An edge-face coloring of a plane graph with edge set E and face set F is a coloring of the elements of E ∪F so that adjacent or incident elements receive different colors. Borodin [Discrete Math 128(1-3): [21][22][23][24][25][26][27][28][29][30][31][32][33] 1994] proved that every plane graph of max

Polychromatic colorings of bounded degre
Polychromatic colorings of bounded degree plane graphs
✍ Elad Horev; Roi Krakovski 📂 Article 📅 2009 🏛 John Wiley and Sons 🌐 English ⚖ 289 KB

## Abstract A __polychromatic k__‐__coloring__ of a plane graph __G__ is an assignment of __k__ colors to the vertices of __G__ such that every face of __G__ has __all k__ colors on its boundary. For a given plane graph __G__, one seeks the __maximum__ number __k__ such that __G__ admits a polychro

Rainbow faces in edge-colored plane grap
Rainbow faces in edge-colored plane graphs
✍ Stanislav Jendrol'; Jozef Miškuf; Roman Soták; Erika Škrabul'áková 📂 Article 📅 2009 🏛 John Wiley and Sons 🌐 English ⚖ 150 KB

## Abstract A face of an edge‐colored plane graph is called __rainbow__ if the number of colors used on its edges is equal to its size. The maximum number of colors used in an edge coloring of a connected plane graph __G__with no rainbow face is called __the edge‐rainbowness__ of __G__. In this pap