Sobre representações graficas orientadas de grupos

Orientador : Claudio Leonardo LucchesiDissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Matematica, Estatistica e Computação CientíficaResumo: Não informadoAbstract: Not informedMestradoMestre em Matemátic

On the classification problem for split graphs

Abstract The Classification Problem is the problem of deciding whether a simple graph has chromatic index equal to Δ or Δ+1. In the first case, the graphs are called Class 1, otherwise, they are Class 2. A split graph is a graph whose vertex set admits a partition into a stable set and a clique. Split graphs are a subclass of chordal graphs. Figueiredo at al. (J. Combin. Math. Combin. Comput. 32:79–91, 2000) state that a chordal graph is Class 2 if and only if it is neighborhood-overfull. In this paper, we give a characterization of neighborhood-overfull split graphs and we show that the above conjecture is true for some split graphs

A lexBFS Algorithm for Proper Interval Graph Recognition

Interval graphs are the intersection graphs of families of intervals in the real line. If the intervals can be chosen so that no interval contains another, we obtain the subclass of proper interval graphs. In this paper, we show how to recognize proper interval graphs with one lexBFS. This algorithm runs in linear time, and produces as a by-product the clique partition of the input graph

Total-Chromatic Number and Chromatic Index of Dually Chordal Graphs

A graph is dually chordal if it is the clique graph of a chordal graph. Alternatively, a graph is dually chordal if it admits a maximum neighbourhood order. This class generalizes known subclasses of chordal graphs such as doubly chordal graphs, strongly chordal graphs and interval graphs. We prove that Vizing's total-colour conjecture holds for dually chordal graphs. We describe a new heuristic that yields an exact total-colouring algorithm for even maximum degree dually chordal graphs and an exact edge-colouring algorithm for odd maximum degree dually chordal graphs. Key words. graph algorithms, chordal graphs, total colouring, edge colouring, clique graphs, maximum neighbourhood ordering. AMS subject classification. 05C85, 05C15, 68R10, 90C27 1 Introduction We consider the problem of total colouring and edge colouring dually chordal graphs. A total colouring of a graph is a colouring of its vertices and edges such that no adjacent vertices, no adjacent edges, and no incident ver..

Edge Colouring Reduced Indifference Graphs

The chromatic index problem -- finding the minimum number of colours required for colouring the edges of a graph -- is still unsolved for indifference graphs, whose vertices can be linearly ordered so that the vertices contained in the same maximal clique are consecutive in this order. Two adjacent vertices are twins if they belong to the same maximal cliques. A graph is reduced if it contains no pair of twin vertices. We prove that every indifference graph having no twin maximum degree vertices is Class 1. We present two decomposition methods for edge colouring reduced indifference graphs. Key words. edge colourings, interval graphs, proper interval graphs, minimum proper interval graphs, reduced proper interval graphs. AMS subject classification. 05C85, 05C15, 68R10, 90C27 Submitted to WG'99 on 27 February 1999. This work was partially supported by CNPq, CAPES, FAEP, FAPESP and FAPERJ, Brazilian research agencies. y Instituto de Matem'atica and COPPE, Universidade Federal do Ri..