Algorithmic Graph Theory and Perfect Graphs Second Edition Martin Charles Golumbic Caesarea Rothschild Institute University of Haifa Haifa, Israel 2004 ELSEVIER .. Amsterdam - Boston - Heidelberg - London - New York - Oxford Paris - San Diego - San Francisco - Singapore - Sydney - … By continuing you agree to the use of cookies. Each of the heuristics produces tree decompositions whose width may be larger than the optimal width. Full text access Corrections and errata to: Algorithmic graph theory and perfect graphs, the original 1980 edition Pages xxiii-xxvi Download PDF

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An $L(2,1)$-labeling of a graph $G$ is a function $f$ from the vertex set $V(G)$ to the set of all nonnegative integers such that $|f(x)-f(y)|\ge 2$ if $d(x,y)=1$ and $|f(x)-f(y)|\ge 1$ if $d(x,y)=2$.

First, we prove that every graph with Dilworth number at most three has a simplical vertex, in the graph or in its complement. Efficient algorithms for various problems based on structural properties of graphs in these classes.

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We prove that the classes of cographs and clique perfect graphs without isolated vertices satisfy the 〈2〉-property and the 〈3〉-property, but do not satisfy the 〈t〉-property for t≥4. In this paper, we give exact formulas of $\lambda(G\cup H)$ and $\lambda(G+H)$. Finally, we present a polynomial time algorithm to determine $\lambda(T)$ for a tree $T$.

For more and more applications, it is important to be able to compute the treewidth of a given graph and to find tree decompositions of small width reasonably fast.

Basic algorithmic techniques for graph problems: graph traversals (DFS and BFS), topological sorting, Eular tours. This paper gives an overview of several upper bound heuristics that have been proposed and tested for the problem of determining the treewidth of a graph and finding tree decompositions.

This book presents the mathematical and algorithmic properties of special classes of perfect graphs. The $L(2,1)$-labeling number $\lambda(G)$ of $G$ is the smallest number $k$ such that $G$ has an $L(2,1)$-labeling with $\max\{f(v):v\in V(G)\}=k$. Second, weprovide a characterization of graphs G with this property: each maximal vertex ofG is simplical in the complement of G. Finally, we introduce the notion of a locally perfect order and show that every arborescence-comparability graph admits a locally perfect order. We also describe the first parallel algorithms for solving the dynamic version of the shortest path problem. PDF | On Jun 1, 1986, Rolf H. Möhring published Algorithmic Graph Theory and Perfect Graphs | Find, read and cite all the research you need on ResearchGate

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