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Tytuł:
Recursively arbitrarily vertex-decomposable graphs
Autorzy:
Baudon, O.
Gilbert, F.
Woźniak, M.
Powiązania:
https://bibliotekanauki.pl/articles/255981.pdf
Data publikacji:
2012
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
arbitrary vertex decomposable (AVD) graph
recursively AVD graphs
Opis:
A graph G = (V, E) is arbitrarily vertex decomposable if for any sequence ϒ of positive integers adding up to/V/, there is a sequence of vertex-disjoint subsets of V whose orders are given by ϒ, and which induce connected graphs. The main aim of this paper is to study the recursive version of this problem. We present a solution for trees, suns, and partially for a class of 2-connected graphs called balloons.
Źródło:
Opuscula Mathematica; 2012, 32, 4; 689-706
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Recursively arbitrarily vertex-decomposable suns
Autorzy:
Baudon, O.
Gilbert, F.
Woźniak, M.
Powiązania:
https://bibliotekanauki.pl/articles/254835.pdf
Data publikacji:
2011
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
arbitrarily vertex-decomposable graphs (AVD)
recursively AVD graphs
Opis:
A graph G = (V,E) is arbitrarily vertex decomposable if for any sequence τ of positive integers adding up to /V /, there is a sequence of vertex-disjoint subsets of V whose orders are given by τ , and which induce connected graphs. The aim of this paper is to study the recursive version of this problem on a special class of graphs called suns. This paper is a complement of [O. Baudon, F. Gilbert, M. Woźniak, Recursively arbitrarily vertex-decomposable graphs, research report, 2010].
Źródło:
Opuscula Mathematica; 2011, 31, 4; 533-547
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
The {−2,−1}-Selfdual and Decomposable Tournaments
Autorzy:
Boudabbous, Youssef
Ille, Pierre
Powiązania:
https://bibliotekanauki.pl/articles/31342271.pdf
Data publikacji:
2018-08-01
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
tournament
decomposable
selfdual
Opis:
We only consider finite tournaments. The dual of a tournament is obtained by reversing all the arcs. A tournament is selfdual if it is isomorphic to its dual. Given a tournament T, a subset X of V (T) is a module of T if each vertex outside X dominates all the elements of X or is dominated by all the elements of X. A tournament T is decomposable if it admits a module X such that 1 < |X| < |V (T)|. We characterize the decomposable tournaments whose subtournaments obtained by removing one or two vertices are selfdual. We deduce the following result. Let T be a non decomposable tournament. If the subtournaments of T obtained by removing two or three vertices are selfdual, then the subtournaments of T obtained by removing a single vertex are not decomposable. Lastly, we provide two applications to tournaments reconstruction.
Źródło:
Discussiones Mathematicae Graph Theory; 2018, 38, 3; 743-789
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
A path(ological) partition problem
Autorzy:
Broere, Izak
Dorfling, Michael
Dunbar, Jean
Frick, Marietjie
Powiązania:
https://bibliotekanauki.pl/articles/744209.pdf
Data publikacji:
1998
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
vertex partition
τ-partitionable
decomposable graph
Opis:
Let τ(G) denote the number of vertices in a longest path of the graph G and let k₁ and k₂ be positive integers such that τ(G) = k₁ + k₂. The question at hand is whether the vertex set V(G) can be partitioned into two subsets V₁ and V₂ such that τ(G[V₁] ) ≤ k₁ and τ(G[V₂] ) ≤ k₂. We show that several classes of graphs have this partition property.
Źródło:
Discussiones Mathematicae Graph Theory; 1998, 18, 1; 113-125
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
The decomposability of additive hereditary properties of graphs
Autorzy:
Broere, Izak
Dorfling, Michael
Powiązania:
https://bibliotekanauki.pl/articles/743814.pdf
Data publikacji:
2000
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
property of graphs
additive
hereditary
decomposable property of graphs
Opis:
An additive hereditary property of graphs is a class of simple graphs which is closed under unions, subgraphs and isomorphisms. If ₁,...,ₙ are properties of graphs, then a (₁,...,ₙ)-decomposition of a graph G is a partition E₁,...,Eₙ of E(G) such that $G[E_i]$, the subgraph of G induced by $E_i$, is in $_i$, for i = 1,...,n. We define ₁ ⊕...⊕ ₙ as the property {G ∈ : G has a (₁,...,ₙ)-decomposition}. A property is said to be decomposable if there exist non-trivial hereditary properties ₁ and ₂ such that = ₁⊕ ₂. We study the decomposability of the well-known properties of graphs ₖ, ₖ, ₖ, ₖ, ₖ, ₖ and $ ^{p}$.
Źródło:
Discussiones Mathematicae Graph Theory; 2000, 20, 2; 281-291
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
On a partial Hadamard fractional integral inclusion
Autorzy:
Cernea, Aurelian
Powiązania:
https://bibliotekanauki.pl/articles/729602.pdf
Data publikacji:
2016
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
Hadamard fractional derivative
integral inclusion
decomposable set
Opis:
We study a class of nonconvex Hadamard fractional integral inclusions and we establish some Filippov type existence results.
Źródło:
Discussiones Mathematicae, Differential Inclusions, Control and Optimization; 2016, 36, 2; 141-153
1509-9407
Pojawia się w:
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Arbitrarily vertex decomposable caterpillars with four or five leaves
Autorzy:
Cichacz, Sylwia
Görlich, Agnieszka
Marczyk, Antoni
Przybyło, Jakub
Woźniak, Mariusz
Powiązania:
https://bibliotekanauki.pl/articles/743967.pdf
Data publikacji:
2006
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
arbitrarily vertex decomposable graphs
trees
caterpillars
star-like trees
Opis:
A graph G of order n is called arbitrarily vertex decomposable if for each sequence (a₁,...,aₖ) of positive integers such that a₁+...+aₖ = n there exists a partition (V₁,...,Vₖ) of the vertex set of G such that for each i ∈ {1,...,k}, $V_i$ induces a connected subgraph of G on $a_i$ vertices. D. Barth and H. Fournier showed that if a tree T is arbitrarily vertex decomposable, then T has maximum degree at most 4. In this paper we give a complete characterization of arbitrarily vertex decomposable caterpillars with four leaves. We also describe two families of arbitrarily vertex decomposable trees with maximum degree three or four.
Źródło:
Discussiones Mathematicae Graph Theory; 2006, 26, 2; 291-305
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
On arbitrarily vertex decomposable unicyclic graphs with dominating cycle
Autorzy:
Cichacz, Sylwia
Zioło, Irmina
Powiązania:
https://bibliotekanauki.pl/articles/743581.pdf
Data publikacji:
2006
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
arbitrarily vertex decomposable graph
dominating cycle
Opis:
A graph G of order n is called arbitrarily vertex decomposable if for each sequence (n₁,...,nₖ) of positive integers such that $∑^k_{i=1} n_i = n$, there exists a partition (V₁,...,Vₖ) of vertex set of G such that for every i ∈ {1,...,k} the set $V_i$ induces a connected subgraph of G on $n_i$ vertices. We consider arbitrarily vertex decomposable unicyclic graphs with dominating cycle. We also characterize all such graphs with at most four hanging vertices such that exactly two of them have a common neighbour.
Źródło:
Discussiones Mathematicae Graph Theory; 2006, 26, 3; 403-412
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Existence results for ϕ-Laplacian Dirichlet BVP of differential inclusions with application to control theory
Autorzy:
Djebali, Smaïl
Ouahab, Abdelghani
Powiązania:
https://bibliotekanauki.pl/articles/729271.pdf
Data publikacji:
2010
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
differential inclusions
boundary value problem
fixed point
compact
convex
nonconvex
decomposable
continuous selection
controllability
Opis:
In this paper, we study ϕ-Laplacian problems for differential inclusions with Dirichlet boundary conditions. We prove the existence of solutions under both convexity and nonconvexity conditions on the multi-valued right-hand side. The nonlinearity satisfies either a Nagumo-type growth condition or an integrably boundedness one. The proofs rely on the Bonhnenblust-Karlin fixed point theorem and the Bressan-Colombo selection theorem respectively. Two applications to a problem from control theory are provided.
Źródło:
Discussiones Mathematicae, Differential Inclusions, Control and Optimization; 2010, 30, 1; 23-49
1509-9407
Pojawia się w:
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Local irregularity conjecture for 2-multigraphs versus cacti
Autorzy:
Grzelec, Igor
Woźniak, Mariusz
Powiązania:
https://bibliotekanauki.pl/articles/29519642.pdf
Data publikacji:
2024
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
locally irregular coloring
decomposable
cactus graphs
2-multigraphs
Opis:
A multigraph is locally irregular if the degrees of the end-vertices of every multiedge are distinct. The locally irregular coloring is an edge coloring of a multigraph G such that every color induces a locally irregular submultigraph of G. A locally irregular colorable multigraph G is any multigraph which admits a locally irregular coloring. We denote by lir(G) the locally irregular chromatic index of a multigraph G, which is the smallest number of colors required in the locally irregular coloring of the locally irregular colorable multigraph G. In case of graphs the definitions are similar. The Local Irregularity Conjecture for 2-multigraphs claims that for every connected graph G, which is not isomorphic to K2, multigraph 2G obtained from G by doubling each edge satisfies lir(2G) ≤ 2. We show this conjecture for cacti. This class of graphs is important for the Local Irregularity Conjecture for 2-multigraphs and the Local Irregularity Conjecture which claims that every locally irregular colorable graph G satisfies lir(G) ≤ 3. At the beginning it has been observed that all not locally irregular colorable graphs are cacti. Recently it has been proved that there is only one cactus which requires 4 colors for a locally irregular coloring and therefore the Local Irregularity Conjecture was disproved.
Źródło:
Opuscula Mathematica; 2024, 44, 1; 49-65
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Existence and solution sets of impulsive functional differential inclusions with multiple delay
Autorzy:
Helal, M.
Ouahab, A.
Powiązania:
https://bibliotekanauki.pl/articles/256052.pdf
Data publikacji:
2012
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
impulsive functional differential inclusions
decomposable set
parameter differential inclusions
AR-set
control theory
Opis:
In this paper, we present some existence results of solutions and study the topological structure of solution sets for the following first-order impulsive neutral functional differential inclusions with initial condition: [formula] where J : = [0; b] and 0 = t0 < t1 < ... < tm < tm+1 = b (m ∈ N*), F is a set-valued map and g is single map. The functions Ik characterize the jump of the solutions at impulse points tk (k = 1, ... m). Our existence result relies on a nonlinear alternative for compact u.s.c. maps. Then, we present some existence results and investigate the compactness of solution sets, some regularity of operator solutions and absolute retract (in short AR). The continuous dependence of solutions on parameters in the convex case is also examined. Applications to a problem from control theory are provided.
Źródło:
Opuscula Mathematica; 2012, 32, 2; 249-283
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Inverse limits on intervals using unimodal bonding maps having only periodic points whose periods are all the powers of two
Autorzy:
Ingram, W.
Roe, Robert
Powiązania:
https://bibliotekanauki.pl/articles/965889.pdf
Data publikacji:
1999
Wydawca:
Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:
hereditarily decomposable continuum
logistic mapping
inverse limit
Opis:
We derive several properties of unimodal maps having only periodic points whose period is a power of 2. We then consider inverse limits on intervals using a single strongly unimodal bonding map having periodic points whose only periods are all the powers of 2. One such mapping is the logistic map, $f_λ(x)$ = 4λx(1-x) on [f(λ),λ], at the Feigenbaum limit, λ ≈ 0.89249. It is known that this map produces an hereditarily decomposable inverse limit with only three topologically different subcontinua. Other examples of such maps are given and it is shown that any two strongly unimodal maps with periodic point whose only periods are all the powers of 2 produce homeomorphic inverse limits whenever each map has the additional property that the critical point lies in the closure of the orbit of the right endpoint of the interval.
Źródło:
Colloquium Mathematicum; 1999, 81, 1; 51-61
0010-1354
Pojawia się w:
Colloquium Mathematicum
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
On some families of arbitrarily vertex decomposable spiders
Autorzy:
Juszczyk, T.
Zioło, I. A.
Powiązania:
https://bibliotekanauki.pl/articles/254779.pdf
Data publikacji:
2010
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
arbitrarily vertex decomposable graph
trees
Opis:
A graph G of order n is called arbitrarily vertex decomposable if for each sequence (n1, . . . , nk) of positive integers such that [formula], there exists a partition (V1, . . . , Vk) of the vertex set of G such that for every i ∈ {1, . . . , k} the set Vi induces a connected subgraph of G on ni vertices. A spider is a tree with one vertex of degree at least 3. We characterize two families of arbitrarily vertex decomposable spiders which are homeomorphic to stars with at most four hanging edges.
Źródło:
Opuscula Mathematica; 2010, 30, 2; 147-154
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Arc-Disjoint Hamiltonian Cycles in Round Decomposable Locally Semicomplete Digraphs
Autorzy:
Li, Ruijuan
Han, Tingting
Powiązania:
https://bibliotekanauki.pl/articles/31342322.pdf
Data publikacji:
2018-05-01
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
locally semicomplete digraph
local tournament
round decomposable
arc-disjoint
Hamiltonian cycle
Hamiltonian path
Opis:
Let D = (V,A) be a digraph; if there is at least one arc between every pair of distinct vertices of D, then D is a semicomplete digraph. A digraph D is locally semicomplete if for every vertex x, the out-neighbours of x induce a semicomplete digraph and the in-neighbours of x induce a semicomplete digraph. A locally semicomplete digraph without 2-cycle is a local tournament. In 2012, Bang-Jensen and Huang [J. Combin Theory Ser. B 102 (2012) 701–714] concluded that every 2-arc-strong locally semicomplete digraph which is not the second power of an even cycle has two arc-disjoint strong spanning subdigraphs, and proposed the conjecture that every 3-strong local tournament has two arc-disjoint Hamiltonian cycles. According to Bang-Jensen, Guo, Gutin and Volkmann, locally semicomplete digraphs have three subclasses: the round decomposable; the non-round decomposable which are not semicomplete; the non-round decomposable which are semicomplete. In this paper, we prove that every 3-strong round decomposable locally semicomplete digraph has two arc-disjoint Hamiltonian cycles, which implies that the conjecture holds for the round decomposable local tournaments. Also, we characterize the 2-strong round decomposable local tournaments each of which contains a Hamiltonian path P and a Hamiltonian cycle arc-disjoint from P.
Źródło:
Discussiones Mathematicae Graph Theory; 2018, 38, 2; 477-490
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Arbitrarily Partitionable {2K2, C4}-Free Graphs
Autorzy:
Liu, Fengxia
Wu, Baoyindureng
Meng, Jixiang
Powiązania:
https://bibliotekanauki.pl/articles/32361721.pdf
Data publikacji:
2022-05-01
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
arbitrarily partitionable graphs
arbitrarily vertex decomposable
threshold graphs
{2 K 2, C 4 }-free graphs
Opis:
A graph G = (V, E) of order n is said to be arbitrarily partitionable if for each sequence λ = (λ1, λ2, …, λp) of positive integers with λ1 + … +λp = n, there exists a partition (V1, V2, … , Vp) of the vertex set V such that Vi induces a connected subgraph of order λi in G for each i ∈ {1, 2, …, p}. In this paper, we show that a threshold graph is arbitrarily partitionable if and only if it admits a perfect matching or a near perfect matching. We also give a necessary and sufficient condition for a {2K2, C4}-free graph being arbitrarily partitionable, as an extension for a result of Broersma, Kratsch and Woeginger [Fully decomposable split graphs, European J. Combin. 34 (2013) 567–575] on split graphs.
Źródło:
Discussiones Mathematicae Graph Theory; 2022, 42, 2; 485-500
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Wyświetlanie 1-15 z 22

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