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    Wyświetlanie 1-13 z 13
    Tytuł:
    The leafage of a chordal graph
    Autorzy:
    Lin, In-Jen
    McKee, Terry
    West, Douglas
    Powiązania:
    https://bibliotekanauki.pl/articles/972051.pdf
    Data publikacji:
    1998
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    chordal graph
    subtree intersection representation
    leafage
    Opis:
    The leafage l(G) of a chordal graph G is the minimum number of leaves of a tree in which G has an intersection representation by subtrees. We obtain upper and lower bounds on l(G) and compute it on special classes. The maximum of l(G) on n-vertex graphs is n - lg n - 1/2 lg lg n + O(1). The proper leafage l*(G) is the minimum number of leaves when no subtree may contain another; we obtain upper and lower bounds on l*(G). Leafage equals proper leafage on claw-free chordal graphs. We use asteroidal sets and structural properties of chordal graphs.
    Źródło:
    Discussiones Mathematicae Graph Theory; 1998, 18, 1; 23-48
    2083-5892
    Pojawia się w:
    Discussiones Mathematicae Graph Theory
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Vertex rainbow colorings of graphs
    Autorzy:
    Fujie-Okamoto, Futaba
    Kolasinski, Kyle
    Lin, Jianwei
    Zhang, Ping
    Powiązania:
    https://bibliotekanauki.pl/articles/743667.pdf
    Data publikacji:
    2012
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    rainbow path
    vertex rainbow coloring
    vertex rainbow connection number
    Opis:
    In a properly vertex-colored graph G, a path P is a rainbow path if no two vertices of P have the same color, except possibly the two end-vertices of P. If every two vertices of G are connected by a rainbow path, then G is vertex rainbow-connected. A proper vertex coloring of a connected graph G that results in a vertex rainbow-connected graph is a vertex rainbow coloring of G. The minimum number of colors needed in a vertex rainbow coloring of G is the vertex rainbow connection number vrc(G) of G. Thus if G is a connected graph of order n ≥ 2, then 2 ≤ vrc(G) ≤ n. We present characterizations of all connected graphs G of order n for which vrc(G) ∈ {2,n-1,n} and study the relationship between vrc(G) and the chromatic number χ(G) of G. For a connected graph G of order n and size m, the number m-n+1 is the cycle rank of G. Vertex rainbow connection numbers are determined for all connected graphs of cycle rank 0 or 1 and these numbers are investigated for connected graphs of cycle rank 2.
    Źródło:
    Discussiones Mathematicae Graph Theory; 2012, 32, 1; 63-80
    2083-5892
    Pojawia się w:
    Discussiones Mathematicae Graph Theory
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    On discontinuous quasi-variational inequalities
    Autorzy:
    Chu, Liang-Ju
    Lin, Ching-Yang
    Powiązania:
    https://bibliotekanauki.pl/articles/729419.pdf
    Data publikacji:
    2007
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    variational inequality
    quasi-variatioal inequality
    Ricceri's conjecture
    Karamardian condition
    Hausdorff continuous multifunction
    Kneser's minimax inequality
    Opis:
    In this paper, we derive a general theorem concerning the quasi-variational inequality problem: find x̅ ∈ C and y̅ ∈ T(x̅) such that x̅ ∈ S(x̅) and
    ⟨y̅,z-x̅⟩ ≥ 0, ∀ z ∈ S(x̅),
    where C,D are two closed convex subsets of a normed linear space X with dual X*, and $T:X → 2^{X*}$ and $S:C → 2^D$ are multifunctions. In fact, we extend the above to an existence result proposed by Ricceri [12] for the case where the multifunction T is required only to satisfy some general assumption without any continuity. Under a kind of Karmardian's condition, we give a partial affirmative answer to an unbounded quasi-variational inequality problem.
    Źródło:
    Discussiones Mathematicae, Differential Inclusions, Control and Optimization; 2007, 27, 2; 199-212
    1509-9407
    Pojawia się w:
    Discussiones Mathematicae, Differential Inclusions, Control and Optimization
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    The signless Laplacian spectral radius of graphs with given number of cut vertices
    Autorzy:
    Cui, Lin
    Fan, Yi-Zheng
    Powiązania:
    https://bibliotekanauki.pl/articles/744527.pdf
    Data publikacji:
    2010
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    graph
    cut vertex
    signless Laplacian matrix
    spectral radius
    Opis:
    In this paper, we determine the graph with maximal signless Laplacian spectral radius among all connected graphs with fixed order and given number of cut vertices.
    Źródło:
    Discussiones Mathematicae Graph Theory; 2010, 30, 1; 85-93
    2083-5892
    Pojawia się w:
    Discussiones Mathematicae Graph Theory
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Variational inequalities in noncompact nonconvex regions
    Autorzy:
    Lin, Ching-Yan
    Chu, Liang-Ju
    Powiązania:
    https://bibliotekanauki.pl/articles/729495.pdf
    Data publikacji:
    2003
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    Nikaidô's coincidence theorem
    variational inequality
    nearly convex
    V₀-Karamardian condition
    Saigal condition
    acyclic multifunction
    algebraic interior
    bounding points
    Opis:
    In this paper, a general existence theorem on the generalized variational inequality problem GVI(T,C,ϕ) is derived by using our new versions of Nikaidô's coincidence theorem, for the case where the region C is noncompact and nonconvex, but merely is a nearly convex set. Equipped with a kind of V₀-Karamardian condition, this general existence theorem contains some existing ones as special cases. Based on a Saigal condition, we also modify the main theorem to obtain another existence theorem on GVI(T,C,ϕ), which generalizes a result of Fang and Peterson.
    Źródło:
    Discussiones Mathematicae, Differential Inclusions, Control and Optimization; 2003, 23, 1; 5-19
    1509-9407
    Pojawia się w:
    Discussiones Mathematicae, Differential Inclusions, Control and Optimization
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    The domination number of $K_n^3$
    Autorzy:
    Georges, John
    Lin, Jianwei
    Mauro, David
    Powiązania:
    https://bibliotekanauki.pl/articles/30148694.pdf
    Data publikacji:
    2014-08-01
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    Cartesian product
    dominating set
    domination number
    Opis:
    Let $K_n^3$ denote the Cartesian product $K_n□K_n□K_n$, where $K_n$ is the complete graph on $n$ vertices. We show that the domination number of $K_n^3$ is $⌈\frac{n^2}{2}⌉$.
    Źródło:
    Discussiones Mathematicae Graph Theory; 2014, 34, 3; 629-632
    2083-5892
    Pojawia się w:
    Discussiones Mathematicae Graph Theory
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Minimum Coverings of Crowns with Cycles and Stars
    Autorzy:
    Lin, Jenq-Jong
    Jou, Min-Jen
    Powiązania:
    https://bibliotekanauki.pl/articles/32361751.pdf
    Data publikacji:
    2022-02-01
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    cycle
    star
    covering
    decomposition
    crown
    Opis:
    Let F, G and H be graphs. A (G, H)-decomposition of F is a partition of the edge set of F into copies of G and copies of H with at least one copy of G and at least one copy of H. For R ⊆ F, a (G, H)-covering of F with padding R is a (G, H)-decomposition of F + E(R). A (G, H)-covering of F with the smallest cardinality is a minimum (G, H)-covering. This paper gives the solution of finding the minimum (Ck, Sk)-covering of the crown Cn,n−1.
    Źródło:
    Discussiones Mathematicae Graph Theory; 2022, 42, 1; 81-88
    2083-5892
    Pojawia się w:
    Discussiones Mathematicae Graph Theory
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Asymptotic Sharpness of Bounds on Hypertrees
    Autorzy:
    Lin, Yi
    Kang, Liying
    Shan, Erfang
    Powiązania:
    https://bibliotekanauki.pl/articles/31341637.pdf
    Data publikacji:
    2017-08-01
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    hypertree
    semicycle in hypergraph
    chain in hypergraph
    Opis:
    The hypertree can be defined in many different ways. Katona and Szabó introduced a new, natural definition of hypertrees in uniform hypergraphs and investigated bounds on the number of edges of the hypertrees. They showed that a $k$-uniform hypertree on $n$ vertices has at most \( \binom{n}{k−1} \) edges and they conjectured that the upper bound is asymptotically sharp. Recently, Szabó verified that the conjecture holds by recursively constructing an infinite sequence of $k$-uniform hypertrees and making complicated analyses for it. In this note we give a short proof of the conjecture by directly constructing a sequence of $k$-uniform $k$-hypertrees.
    Źródło:
    Discussiones Mathematicae Graph Theory; 2017, 37, 3; 789-795
    2083-5892
    Pojawia się w:
    Discussiones Mathematicae Graph Theory
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    New versions on Nikaidôs coincidence theorem
    Autorzy:
    Chu, Liang-Ju
    Lin, Ching-Yan
    Powiązania:
    https://bibliotekanauki.pl/articles/729530.pdf
    Data publikacji:
    2002
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    Vietoris map
    Nikaidô's coincidence theorem
    Fan-type element
    Górniewicz-type fixed point theorem
    coincidence
    variational inequality
    acyclic multifunction
    partition of unity
    local intersection property
    KKM mapping
    locally selectionable multifunction
    Opis:
    In 1959, Nikaidô established a remarkable coincidence theorem in a compact Hausdorff topological space, to generalize and to give a unified treatment to the results of Gale regarding the existence of economic equilibrium and the theorems in game problems. The main purpose of the present paper is to deduce several generalized key results based on this very powerful result, together with some KKM property. Indeed, we shall simplify and reformulate a few coincidence theorems on acyclic multifunctions, as well as some Górniewicz-type fixed point theorems. Beyond the realm of monotonicity nor metrizability, the results derived here generalize and unify various earlier ones from the classic optimization theory. In the sequel, we shall deduce two versions of Nikaidô's coincidence theorem about Vietoris maps from different approaches.
    Źródło:
    Discussiones Mathematicae, Differential Inclusions, Control and Optimization; 2002, 22, 1; 79-95
    1509-9407
    Pojawia się w:
    Discussiones Mathematicae, Differential Inclusions, Control and Optimization
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Total Colorings of Embedded Graphs with No 3-Cycles Adjacent to 4-Cycles
    Autorzy:
    Wang, Bing
    Wu, Jian-Liang
    Sun, Lin
    Powiązania:
    https://bibliotekanauki.pl/articles/31342246.pdf
    Data publikacji:
    2018-11-01
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    total coloring
    embedded graph
    cycle
    Opis:
    A total-k-coloring of a graph G is a coloring of V ∪ E using k colors such that no two adjacent or incident elements receive the same color. The total chromatic number χ′′(G) of G is the smallest integer k such that G has a total-k-coloring. Let G be a graph embedded in a surface of Euler characteristic ε ≥ 0. If G contains no 3-cycles adjacent to 4-cycles, that is, no 3-cycle has a common edge with a 4-cycle, then χ′′(G) ≤ max{8, Δ+1}.
    Źródło:
    Discussiones Mathematicae Graph Theory; 2018, 38, 4; 977-989
    2083-5892
    Pojawia się w:
    Discussiones Mathematicae Graph Theory
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    On Edge Colorings of 1-Planar Graphs without 5-Cycles with Two Chords
    Autorzy:
    Sun, Lin
    Wu, Jianliang
    Powiązania:
    https://bibliotekanauki.pl/articles/31343454.pdf
    Data publikacji:
    2019-05-01
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    1-planar graphs
    edge coloring
    discharging method
    Opis:
    A graph is 1-planar if it can be drawn on the plane so that each edge is crossed by at most one other edge. In this paper, it is proved that every 1-planar graph with maximum degree ∆ ≥ 8 is edge-colorable with ∆ colors if each of its 5-cycles contains at most one chord.
    Źródło:
    Discussiones Mathematicae Graph Theory; 2019, 39, 2; 301-312
    2083-5892
    Pojawia się w:
    Discussiones Mathematicae Graph Theory
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Core Index of Perfect Matching Polytope for a 2-Connected Cubic Graph
    Autorzy:
    Wang, Xiumei
    Lin, Yixun
    Powiązania:
    https://bibliotekanauki.pl/articles/31343794.pdf
    Data publikacji:
    2018-02-01
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    Fulkerson’s conjecture
    Fan-Raspaud conjecture
    cubic graph
    perfect matching polytope
    core index
    Opis:
    For a 2-connected cubic graph $G$, the perfect matching polytope $P(G)$ of $G$ contains a special point \( x^c = ( \tfrac{1}{3},\tfrac{1}{3},…,\tfrac{1}{3}) \). The core index $ \phi(P(G)) $ of the polytope $P(G)$ is the minimum number of vertices of $P(G)$ whose convex hull contains $ x^c$. The Fulkerson’s conjecture asserts that every 2-connected cubic graph $G$ has six perfect matchings such that each edge appears in exactly two of them, namely, there are six vertices of $P(G)$ such that $ x^c $ is the convex combination of them, which implies that $ \phi(P(G)) \le 6 $. It turns out that the latter assertion in turn implies the Fan-Raspaud conjecture: In every 2-connected cubic graph $G$, there are three perfect matchings $M_1$, $M_2$, and $M_3$ such that $M_1 \cap M_2 \cap M_3 = \emptyset $. In this paper we prove the Fan-Raspaud conjecture for $ \phi(P(G)) \le 12 $ with certain dimensional conditions.
    Źródło:
    Discussiones Mathematicae Graph Theory; 2018, 38, 1; 189-201
    2083-5892
    Pojawia się w:
    Discussiones Mathematicae Graph Theory
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    The List Edge Coloring and List Total Coloring of Planar Graphs with Maximum Degree at Least 7
    Autorzy:
    Sun, Lin
    Wu, Jianliang
    Wang, Bing
    Liu, Bin
    Powiązania:
    https://bibliotekanauki.pl/articles/31348158.pdf
    Data publikacji:
    2020-11-01
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    planar graph
    list edge coloring
    list total coloring
    Opis:
    A graph $G$ is edge $k$-choosable (respectively, total $k$-choosable) if, whenever we are given a list $L(x)$ of colors with $|L(x)| = k$ for each $x ∈ E(G) (x ∈ E(G) ∪ V (G))$, we can choose a color from $L(x)$ for each element $x$ such that no two adjacent (or incident) elements receive the same color. The list edge chromatic index $χ_l^′(G)$ (respectively, the list total chromatic number $χ_l^{′′}(G))$ of $G$ is the smallest integer $k$ such that $G$ is edge (respectively, total) $k$-choosable. In this paper, we focus on a planar graph $G$, with maximum degree $Δ (G) ≥ 7$ and with some structural restrictions, satisfies $χ_l^′(G) = Δ (G)$ and $χ_l^{′′}(G) = Δ (G) + 1$.
    Źródło:
    Discussiones Mathematicae Graph Theory; 2020, 40, 4; 1005-1024
    2083-5892
    Pojawia się w:
    Discussiones Mathematicae Graph Theory
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
      Wyświetlanie 1-13 z 13

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