منابع مشابه
A Linear-time Recognition Algorithm for P4- a Unique Tree Representation for P4-sparse
7)) algorithm for the 3-clique-width problem. Preprint, 1998. Sha98] A. Sharell. Complexit e Descriptive et l'approximation des fonctions de d enombrement. J. Makowsky and U. Rotics. On the cliquewidth of graphs with few P4's. Linear time solvable optimization problems on certain structured graph families, extended abstract. Cou99] B. Courcelle. The monadic second order logic of graphs, XIV: un...
متن کاملLaplacian integrality in P4-sparse and P4-extendible graphs
Let G be a simple graph and L = L(G) the Laplacian matrix of G. G is called L-integral if all its Laplacian eigenvalues are integer numbers. It is known that every cograph, a graph free of P4, is L-integral. The class of P4-sparse graphs and the class of P4-extendible graphs contain the cographs. It seems natural to investigate if the graphs in these classes are still L-integral. In this paper ...
متن کاملMinimum Sum Coloring of P4-sparse graphs
In this paper, we study the Minimum Sum Coloring (MSC) problem on P4-sparse graphs. In the MSC problem, we aim to assign natural numbers to vertices of a graph such that adjacent vertices get different numbers, and the sum of the numbers assigned to the vertices is minimum. First, we introduce the concept of maximal sequence associated with an optimal solution of the MSC problem of any graph. N...
متن کاملWeighted Coloring on P4-sparse Graphs
Given an undirected graph G = (V, E) and a weight function w : V → R, a vertex coloring of G is a partition of V into independent sets, or color classes. The weight of a vertex coloring of G is defined as the sum of the weights of its color classes, where the weight of a color class is the weight of a heaviest vertex belonging to it. In the W C problem, we want to determine the mi...
متن کاملMinimal separators in P4-sparse graphs
In this paper, we determine the minimal separators of P4-sparse graphs and establish bounds on their number. Specifically, we show that a P4-sparse graph G on n vertices and m edges has fewer than 2n/3 minimal separators of total description size at most 4m/3. The bound on the number of minimal separators is tight and is also tight for the class of cographs, a well known subclass of the P4-spar...
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ژورنال
عنوان ژورنال: Discrete Applied Mathematics
سال: 1992
ISSN: 0166-218X
DOI: 10.1016/0166-218x(92)90036-a