Relative colorings of graphs

T-colorings of graphs

✍ Daphne Der-Fen Liu 📂 Article 📅 1992 🏛 Elsevier Science 🌐 English ⚖ 594 KB

Given a finite set T of positive integers containing {0}, a T-coloring of a simple graph G is a nonnegative integer function f defined on the vertex set of G, such that if (u, v} E E(G) then Lf(u) -f (u)l $ T. The T-span of a T-coloring is defined as the difference of the largest and smallest colors

Oriented list colorings of graphs

✍ Zs. Tuza; M. Voigt 📂 Article 📅 2001 🏛 John Wiley and Sons 🌐 English ⚖ 159 KB 👁 1 views

A 2-assignment on a graph G (V,E) is a collection of pairs Lv of allowed colors speci®ed for all vertices v PV. The graph G (with at least one edge) is said to have oriented choice number 2 if it admits an orientation which satis®es the following property: For every 2-assignment there exists a choic

Acrylic improper colorings of graphs

✍ Boiron, P.; Sopena, E.; Vignal, L. 📂 Article 📅 1999 🏛 John Wiley and Sons 🌐 English ⚖ 153 KB 👁 2 views

In this article, we introduce the new notion of acyclic improper colorings of graphs. An improper coloring of a graph is a vertex-coloring in which adjacent vertices are allowed to have the same color, but each color class V i satisfies some condition depending on i. Such a coloring is acyclic if th

Acyclic edge colorings of graphs

✍ Noga Alon; Benny Sudakov; Ayal Zaks 📂 Article 📅 2001 🏛 John Wiley and Sons 🌐 English ⚖ 102 KB

## Abstract A proper coloring of the edges of a graph __G__ is called __acyclic__ if there is no 2‐colored cycle in __G__. The __acyclic edge chromatic number__ of __G__, denoted by __a′__(__G__), is the least number of colors in an acyclic edge coloring of __G__. For certain graphs __G__, __a′__(_

Face colorings of embedded graphs

✍ Dan Archdeacon 📂 Article 📅 1984 🏛 John Wiley and Sons 🌐 English ⚖ 498 KB

We characterize those graphs which have at least one embedding into some surface such that the faces can be properly colored in four or fewer colors. Embeddings into both orientable and nonorientable surfaces are considered.

Circular colorings of weighted graphs

✍ Deuber, Walter A.; Zhu, Xuding 📂 Article 📅 1996 🏛 John Wiley and Sons 🌐 English ⚖ 776 KB

Suppose that G is a finite simple graph and w is a weight function which assigns to each vertex of G a nonnegative real number. Let C be a circle of length t . A t-circular coloring of (G,w) is a mapping A of the vertices of G to arcs of C such that A(%) n A(y) = 0 if (x, y) E E ( G ) and A(x) has l