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    Wyświetlanie 1-2 z 2
    Tytuł:
    Efficient algorithms for minimal disjoint path problems on chordal graphs
    Autorzy:
    Gopalakrishnan, C.
    Satyan, C.
    Pandu Rangan, C.
    Powiązania:
    https://bibliotekanauki.pl/articles/972049.pdf
    Data publikacji:
    1995
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    chordal graph
    minimal paths
    disjoint paths
    clique
    bfs
    Opis:
    Disjoint paths have applications in establishing bottleneck-free communication between processors in a network. The problem of finding minimum delay disjoint paths in a network directly reduces to the problem of finding the minimal disjoint paths in the graph which models the network. Previous results for this problem on chordal graphs were an O(|V| |E|²) algorithm for 2 edge disjoint paths and an O(|V| |E|) algorithm for 2 vertex disjoint paths. In this paper, we give an O(|V| |E|) algorithm for 2 vertex disjoint paths and an O(|V|+|E|) algorithm for 2 edge disjoint paths, which is a significant improvement over the previous result.
    Źródło:
    Discussiones Mathematicae Graph Theory; 1995, 15, 2; 119-145
    2083-5892
    Pojawia się w:
    Discussiones Mathematicae Graph Theory
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    On dually compact closed classes of graphs and BFS-constructible graphs
    Autorzy:
    Polat, Norbert
    Powiązania:
    https://bibliotekanauki.pl/articles/743184.pdf
    Data publikacji:
    2003
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    infinite graph
    dismantlable graph
    constructible graph
    BFS-cons-tructible graph
    variety
    weak-retract
    strong product
    bridged graph
    Helly graph
    weakly-modular graph
    dually compact closed class
    Opis:
    A class C of graphs is said to be dually compact closed if, for every infinite G ∈ C, each finite subgraph of G is contained in a finite induced subgraph of G which belongs to C. The class of trees and more generally the one of chordal graphs are dually compact closed. One of the main part of this paper is to settle a question of Hahn, Sands, Sauer and Woodrow by showing that the class of bridged graphs is dually compact closed. To prove this result we use the concept of constructible graph. A (finite or infinite) graph G is constructible if there exists a well-ordering ≤ (called constructing ordering) of its vertices such that, for every vertex x which is not the smallest element, there is a vertex y < x which is adjacent to x and to every neighbor z of x with z < x. Finite graphs are constructible if and only if they are dismantlable. The case is different, however, with infinite graphs. A graph G for which every breadth-first search of G produces a particular constructing ordering of its vertices is called a BFS-constructible graph. We show that the class of BFS-constructible graphs is a variety (i.e., it is closed under weak retracts and strong products), that it is a subclass of the class of weakly modular graphs, and that it contains the class of bridged graphs and that of Helly graphs (bridged graphs being very special instances of BFS-constructible graphs). Finally we show that the class of interval-finite pseudo-median graphs (and thus the one of median graphs) and the class of Helly graphs are dually compact closed, and that moreover every finite subgraph of an interval-finite pseudo-median graph (resp. a Helly graph) G is contained in a finite isometric pseudo-median (resp. Helly) subgraph of G. We also give two sufficient conditions so that a bridged graph has a similar property.
    Źródło:
    Discussiones Mathematicae Graph Theory; 2003, 23, 2; 365-381
    2083-5892
    Pojawia się w:
    Discussiones Mathematicae Graph Theory
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
      Wyświetlanie 1-2 z 2

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