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    Wyświetlanie 1-5 z 5
    Tytuł:
    A note on uniquely H-colourable graphs
    Autorzy:
    Bonato, Anthony
    Powiązania:
    https://bibliotekanauki.pl/articles/743653.pdf
    Data publikacji:
    2007
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    graph homomorphisms
    core graphs
    uniquely H-colourable
    Opis:
    For a graph H, we compare two notions of uniquely H-colourable graphs, where one is defined via automorphisms, the second by vertex partitions. We prove that the two notions of uniquely H-colourable are not identical for all H, and we give a condition for when they are identical. The condition is related to the first homomorphism theorem from algebra.
    Źródło:
    Discussiones Mathematicae Graph Theory; 2007, 27, 1; 39-44
    2083-5892
    Pojawia się w:
    Discussiones Mathematicae Graph Theory
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Structural results on maximal k-degenerate graphs
    Autorzy:
    Bickle, Allan
    Powiązania:
    https://bibliotekanauki.pl/articles/743285.pdf
    Data publikacji:
    2012
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    k-degenerate
    k-core
    k-tree
    degree sequence
    Ramsey number
    Opis:
    A graph is k-degenerate if its vertices can be successively deleted so that when deleted, each has degree at most k. These graphs were introduced by Lick and White in 1970 and have been studied in several subsequent papers. We present sharp bounds on the diameter of maximal k-degenerate graphs and characterize the extremal graphs for the upper bound. We present a simple characterization of the degree sequences of these graphs and consider related results. Considering edge coloring, we conjecture that a maximal k-degenerate graph is class two if and only if it is overfull, and prove this in some special cases. We present some results on decompositions and arboricity of maximal k-degenerate graphs and provide two characterizations of the subclass of k-trees as maximal k-degenerate graphs. Finally, we define and prove a formula for the Ramsey core numbers.
    Źródło:
    Discussiones Mathematicae Graph Theory; 2012, 32, 4; 659-676
    2083-5892
    Pojawia się w:
    Discussiones Mathematicae Graph Theory
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    On universal graphs for hom-properties
    Autorzy:
    Mihók, Peter
    Miškuf, Jozef
    Semanišin, Gabriel
    Powiązania:
    https://bibliotekanauki.pl/articles/744408.pdf
    Data publikacji:
    2009
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    universal graph
    weakly universal graph
    hom-property
    core
    Opis:
    A graph property is any isomorphism closed class of simple graphs. For a simple finite graph H, let → H denote the class of all simple countable graphs that admit homomorphisms to H, such classes of graphs are called hom-properties. Given a graph property , a graph G ∈ is universal in if each member of is isomorphic to an induced subgraph of G. In particular, we consider universal graphs in → H and we give a new proof of the existence of a universal graph in → H, for any finite graph H.
    Źródło:
    Discussiones Mathematicae Graph Theory; 2009, 29, 2; 401-409
    2083-5892
    Pojawia się w:
    Discussiones Mathematicae Graph Theory
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    The Quest for A Characterization of Hom-Properties of Finite Character
    Autorzy:
    Broere, Izak
    Matsoha, Moroli D.V.
    Heidema, Johannes
    Powiązania:
    https://bibliotekanauki.pl/articles/31340894.pdf
    Data publikacji:
    2016-05-01
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    (countable) graph
    homomorphism (of graphs)
    property of graphs
    hom-property
    (finitely-)induced-hereditary property
    finitely determined property
    (weakly) finite character
    axiomatizable property
    compactness theorems
    core
    connectedness
    chromatic number
    clique number
    independence number
    dominating set
    Opis:
    A graph property is a set of (countable) graphs. A homomorphism from a graph \( G \) to a graph \( H \) is an edge-preserving map from the vertex set of \( G \) into the vertex set of \( H \); if such a map exists, we write \( G \rightarrow H \). Given any graph \( H \), the hom-property \( \rightarrow H \) is the set of \( H \)-colourable graphs, i.e., the set of all graphs \( G \) satisfying \( G \rightarrow H \). A graph property \( mathcal{P} \) is of finite character if, whenever we have that \( F \in \mathcal{P} \) for every finite induced subgraph \( F \) of a graph \( G \), then we have that \( G \in \mathcal{P} \) too. We explore some of the relationships of the property attribute of being of finite character to other property attributes such as being finitely-induced-hereditary, being finitely determined, and being axiomatizable. We study the hom-properties of finite character, and prove some necessary and some sufficient conditions on \( H \) for \( \rightarrow H \) to be of finite character. A notable (but known) sufficient condition is that \( H \) is a finite graph, and our new model-theoretic proof of this compactness result extends from hom-properties to all axiomatizable properties. In our quest to find an intrinsic characterization of those \( H \) for which \( \rightarrow H \) is of finite character, we find an example of an infinite connected graph with no finite core and chromatic number 3 but with hom-property not of finite character.
    Źródło:
    Discussiones Mathematicae Graph Theory; 2016, 36, 2; 479-500
    2083-5892
    Pojawia się w:
    Discussiones Mathematicae Graph Theory
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Existence of Regular Nut Graphs for Degree at Most 11
    Autorzy:
    Fowler, Patrick W.
    Gauci, John Baptist
    Goedgebeur, Jan
    Pisanski, Tomaž
    Sciriha, Irene
    Powiązania:
    https://bibliotekanauki.pl/articles/31550028.pdf
    Data publikacji:
    2020-05-01
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    nut graph
    core graph
    regular graph
    nullity
    Opis:
    A nut graph is a singular graph with one-dimensional kernel and corresponding eigenvector with no zero elements. The problem of determining the orders n for which d-regular nut graphs exist was recently posed by Gauci, Pisanski and Sciriha. These orders are known for d ≤ 4. Here we solve the problem for all remaining cases d ≤ 11 and determine the complete lists of all d-regular nut graphs of order n for small values of d and n. The existence or non-existence of small regular nut graphs is determined by a computer search. The main tool is a construction that produces, for any d-regular nut graph of order n, another d-regular nut graph of order n+2d. If we are given a sufficient number of d-regular nut graphs of consecutive orders, called seed graphs, this construction may be applied in such a way that the existence of all d-regular nut graphs of higher orders is established. For even d the orders n are indeed consecutive, while for odd d the orders n are consecutive even numbers. Furthermore, necessary conditions for combinations of order and degree for vertex-transitive nut graphs are derived.
    Źródło:
    Discussiones Mathematicae Graph Theory; 2020, 40, 2; 533-557
    2083-5892
    Pojawia się w:
    Discussiones Mathematicae Graph Theory
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
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