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Full 4-colorings of 4-regular maps

✍ Scribed by Kenneth A. Berman; H. Shank

Publisher
John Wiley and Sons
Year
1979
Tongue
English
Weight
181 KB
Volume
3
Category
Article
ISSN
0364-9024

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✦ Synopsis

Abstract

A full coloring of a planar map is a face coloring such that all the faces at ech vertex are colored differently. In this paper the planar 4‐regular maps which have a full 4‐coloring are characterized. This leads to a characterization of the planar maps (not necessarily 4‐valent) which have a coupled 4‐coloring.

📜 SIMILAR VOLUMES

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✍ François Jaeger; Gerhard Koester 📂 Article 📅 1990 🏛 John Wiley and Sons 🌐 English ⚖ 231 KB 👁 1 views

## Abstract We associate partitions of the edge‐set of a 4‐regular plane graph into 1‐factors or 2‐factors to certain 3‐valued vertex signatures in the spirit of the work by H. Grötzsch [1]. As a corollary we obtain a simple proof of a result of F. Jaeger and H. Shank [2] on the edge‐4‐colorability

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## Abstract A (plane) 4‐regular map __G__ is called __C__‐simple if it arises as a superposition of simple closed curves (tangencies are not allowed); in this case σ (__G__) is the smallest integer __k__ such that the curves of __G__ can be colored with __k__ colors in such a way that no two curves

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✍ F. Jaeger; H. Shank 📂 Article 📅 1982 🏛 John Wiley and Sons 🌐 English ⚖ 37 KB 👁 1 views

On p. 272 of the above article, paragraph # 3 is incomplete. It should read as the following: Hence to prove Proposition 4 it is enough to show that the edges of Q 4 can be colored with 4 colors in such a way that each square has one edge of each color. Such a coloring is displayed on the following

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✍ Herbert Fleischner; Gert Sabidussi 📂 Article 📅 2003 🏛 John Wiley and Sons 🌐 English ⚖ 187 KB 👁 1 views

## Abstract On the model of the cycle‐plus‐triangles theorem, we consider the problem of 3‐colorability of those 4‐regular hamiltonian graphs for which the components of the edge‐complement of a given hamiltonian cycle are non‐selfcrossing cycles of constant length ≥ 4. We show that this problem is

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✍ Han Ren; Yanpei Liu; Zhaoxiang Li 📂 Article 📅 2002 🏛 Elsevier Science 🌐 English ⚖ 195 KB

In this paper rooted (near-) 4-regular maps on the plane are counted with respect to the root-valency, the number of edges, the number of inner faces, the number of non-root vertex loops, the number of non-root vertex blocks, and the number of multi-edges. As special cases, formulae of several types