Coloring of universal graphs

Star coloring of graphs

✍ Guillaume Fertin; André Raspaud; Bruce Reed 📂 Article 📅 2004 🏛 John Wiley and Sons 🌐 English ⚖ 181 KB

## Abstract A __star coloring__ of an undirected graph __G__ is a proper vertex coloring of __G__ (i.e., no two neighbors are assigned the same color) such that any path of length 3 in __G__ is not bicolored. The __star chromatic number__ of an undirected graph __G__, denoted by χ~s~(__G__), is the

Linear coloring of graphs

✍ Raphael Yuster 📂 Article 📅 1998 🏛 Elsevier Science 🌐 English ⚖ 213 KB

A proper vertex coloring of a graph is called linear if the subgraph induced by the vertices colored by any two colors is a set of vertex-disjoint paths. The linear chromatic number of a graph G, denoted by lc(G), is the minimum number of colors in a linear coloring of G. Extending a result of Alon,

Universal graphs and induced-universal g

Universal graphs and induced-universal graphs

✍ Fan R. K. Chung 📂 Article 📅 1990 🏛 John Wiley and Sons 🌐 English ⚖ 484 KB

## Abstract We construct graphs that contain all bounded‐degree trees on __n__ vertices as induced subgraphs and have only __cn__ edges for some constant __c__ depending only on the maximum degree. In general, we consider the problem of determining the graphs, so‐called universal graphs (or induced

Coloring edges of embedded graphs

✍ Daniel P. Sanders; Yue Zhao 📂 Article 📅 2000 🏛 John Wiley and Sons 🌐 English ⚖ 80 KB 👁 2 views

In this paper, we prove that any graph G with maximum degree ÁG ! 11 p 49À241AEa2, which is embeddable in a surface AE of characteristic 1AE 1 and satis®es jVGj b 2ÁGÀ5À2 p 6ÁG, is class one.

Balanced coloring of bipartite graphs

✍ Uriel Feige; Shimon Kogan 📂 Article 📅 2009 🏛 John Wiley and Sons 🌐 English ⚖ 128 KB

## Abstract Given a bipartite graph __G__(__U__∪__V, E__) with __n__ vertices on each side, an independent set __I__∈__G__ such that |__U__∩__I__|=|__V__∩__I__| is called a balanced bipartite independent set. A balanced coloring of __G__ is a coloring of the vertices of __G__ such that each color c

Star coloring of sparse graphs

✍ Yuehua Bu; Daniel W. Cranston; Mickaël Montassier; André Raspaud; Weifan Wang 📂 Article 📅 2009 🏛 John Wiley and Sons 🌐 English ⚖ 174 KB

## Abstract A proper coloring of the vertices of a graph is called a __star coloring__ if the union of every two color classes induces a star forest. The star chromatic number χ~__s__~(__G__) is the smallest number of colors required to obtain a star coloring of __G__. In this paper, we study the r