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    Wyświetlanie 1-4 z 4
    Tytuł:
    On the structure of compact graphs
    Autorzy:
    Nikandish, R.
    Shaveisi, F.
    Powiązania:
    https://bibliotekanauki.pl/articles/255638.pdf
    Data publikacji:
    2017
    Wydawca:
    Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
    Tematy:
    compact graph
    vertex degree
    cycle
    neighborhood
    Opis:
    A simple graph G is called a compact graph if G contains no isolated vertices and for each pair x, y of non-adjacent vertices of G, there is a vertex z with N(x) ∪ N(y) ⊆ N(z), where N(v) is the neighborhood of v, for every vertex v of G. In this paper, compact graphs with sufficient number of edges are studied. Also, it is proved that every regular compact graph is strongly regular. Some results about cycles in compact graphs are proved, too. Among other results, it is proved that if the ascending chain condition holds for the set of neighbors of a compact graph G, then the descending chain condition holds for the set of neighbors of G.
    Źródło:
    Opuscula Mathematica; 2017, 37, 6; 875-886
    1232-9274
    2300-6919
    Pojawia się w:
    Opuscula Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    A note on $PM$-compact bipartite graphs
    Autorzy:
    Liu, Jinfeng
    Wang, Xiumei
    Powiązania:
    https://bibliotekanauki.pl/articles/31232003.pdf
    Data publikacji:
    2014-05-01
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    perfect matching
    PM-compact graph
    matching-covered graph
    Opis:
    A graph is called perfect matching compact (briefly, PM-compact), if its perfect matching graph is complete. Matching-covered PM-compact bipartite graphs have been characterized. In this paper, we show that any PM-compact bipartite graph G with δ (G) ≥ 2 has an ear decomposition such that each graph in the decomposition sequence is also PM-compact, which implies that G is matching-covered
    Źródło:
    Discussiones Mathematicae Graph Theory; 2014, 34, 2; 409-413
    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
    Tytuł:
    Best approximations, fixed points and parametric projections
    Autorzy:
    Cardinali, Tiziana
    Powiązania:
    https://bibliotekanauki.pl/articles/729491.pdf
    Data publikacji:
    2002
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    fixed point
    parametric projection
    best approximation
    upper semicontinuous
    partially closed graph
    f-approximatively compact
    Oshman space
    Opis:
    If f is a continuous seminorm, we prove two f-best approximation theorems for functions Φ not necessarily continuous as a consequence of our version of Glebov's fixed point theorem. Moreover, we obtain another fixed point theorem that improves a recent result of [4]. In the last section, we study continuity-type properties of set valued parametric projections and our results improve recent theorems due to Mabizela [11].
    Źródło:
    Discussiones Mathematicae, Differential Inclusions, Control and Optimization; 2002, 22, 2; 243-260
    1509-9407
    Pojawia się w:
    Discussiones Mathematicae, Differential Inclusions, Control and Optimization
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
      Wyświetlanie 1-4 z 4

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