𝔖 Bobbio Scriptorium
✦   LIBER   ✦

On the use of alternating chains and hypergraphs in edge coloring

✍ Scribed by D. de Werra

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

No coin nor oath required. For personal study only.

✦ Synopsis

Abstract

Existence of some generalized edge colorings is proved by using the properties of hypergraphs as well as alternating chain methods. A general framework is given for edge colorings and some general properties of balancing are derived.

πŸ“œ SIMILAR VOLUMES

On the Number of Edges in Hypergraphs Cr
On the Number of Edges in Hypergraphs Critical with Respect to Strong Colourings
✍ Alexandr V. Kostochka; Douglas R. Woodall πŸ“‚ Article πŸ“… 2000 πŸ› Elsevier Science 🌐 English βš– 94 KB

A colouring of the vertices of a hypergraph G is called strong if, for every edge A, the colours of all vertices in A are distinct. It corresponds to a colouring of the generated graph (G) obtained from G by replacing every edge by a clique. We estimate the minimum number of edges possible in a k-cr

On the edge-coloring problem for a class
On the edge-coloring problem for a class of 4-regular maps
✍ F. Jaeger; H. Shank πŸ“‚ Article πŸ“… 1981 πŸ› John Wiley and Sons 🌐 English βš– 300 KB πŸ‘ 1 views

## 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 Οƒ (__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

Erratum: On the edge-coloring problem fo
Erratum: On the edge-coloring problem for a class of 4-regular maps
✍ F. Jaeger; H. Shank πŸ“‚ Article πŸ“… 1982 πŸ› John Wiley and Sons 🌐 English βš– 37 KB πŸ‘ 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

On the Use of the Logistic Equation in M
On the Use of the Logistic Equation in Models of Food Chains
✍ B.W. Kooi; M.P. Boer; S.A.L.M. Kooijman πŸ“‚ Article πŸ“… 1998 πŸ› Springer 🌐 English βš– 229 KB

In food chain models the lowest trophic level is often assumed to grow logistically. Anomalous behaviour of the solution of the logistic equation and problems with the introduction of mortality have recently been reported. As predation on the lowest trophic level is a kind of mortality, one expects

NP-completeness of list coloring and pre
NP-completeness of list coloring and precoloring extension on the edges of planar graphs
✍ DΓ‘niel Marx πŸ“‚ Article πŸ“… 2005 πŸ› John Wiley and Sons 🌐 English βš– 110 KB

## Abstract In the edge precoloring extension problem, we are given a graph with some of the edges having preassigned colors and it has to be decided whether this coloring can be extended to a proper __k__‐edge‐coloring of the graph. In list edge coloring every edge has a list of admissible colors,