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Tytuł:
Cardinality of a minimal forbidden graph family for reducible additive hereditary graph properties
Autorzy:
Drgas-Burchardt, Ewa
Powiązania:
https://bibliotekanauki.pl/articles/743169.pdf
Data publikacji:
2009
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
hereditary graph property
lattice of additive hereditary graph properties
minimal forbidden graph family
join in the lattice
reducibility
Opis:
An additive hereditary graph property is any class of simple graphs, which is closed under isomorphisms unions and taking subgraphs. Let $L^a$ denote a class of all such properties. In the paper, we consider H-reducible over $L^a$ properties with H being a fixed graph. The finiteness of the sets of all minimal forbidden graphs is analyzed for such properties.
Źródło:
Discussiones Mathematicae Graph Theory; 2009, 29, 2; 263-274
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Forbidden Structures for Planar Perfect Consecutively Colourable Graphs
Autorzy:
Borowiecka-Olszewska, Marta
Drgas-Burchardt, Ewa
Powiązania:
https://bibliotekanauki.pl/articles/31341980.pdf
Data publikacji:
2017-05-01
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
edge colouring
consecutive (interval) colouring
deficiency
Sevastjanov graph
forbidden graph
Opis:
A consecutive colouring of a graph is a proper edge colouring with posi- tive integers in which the colours of edges incident with each vertex form an interval of integers. The idea of this colouring was introduced in 1987 by Asratian and Kamalian under the name of interval colouring. Sevast- janov showed that the corresponding decision problem is NP-complete even restricted to the class of bipartite graphs. We focus our attention on the class of consecutively colourable graphs whose all induced subgraphs are consecutively colourable, too. We call elements of this class perfect consecutively colourable to emphasise the conceptual similarity to perfect graphs. Obviously, the class of perfect consecutively colourable graphs is induced hereditary, so it can be characterized by the family of induced forbidden graphs. In this work we give a necessary and sufficient conditions that must be satisfied by the generalized Sevastjanov rosette to be an induced forbid- den graph for the class of perfect consecutively colourable graphs. Along the way, we show the exact values of the deficiency of all generalized Sevastjanov rosettes, which improves the earlier known estimating result. It should be mentioned that the deficiency of a graph measures its closeness to the class of consecutively colourable graphs. We motivate the investigation of graphs considered here by showing their connection to the class of planar perfect consecutively colourable graphs.
Źródło:
Discussiones Mathematicae Graph Theory; 2017, 37, 2; 315-336
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Minimal forbidden subgraphs of reducible graph properties
Autorzy:
Berger, Amelie
Powiązania:
https://bibliotekanauki.pl/articles/743439.pdf
Data publikacji:
2001
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
reducible graph properties
forbidden subgraphs
induced subgraphs
Opis:
A property of graphs is any class of graphs closed under isomorphism. Let ₁,₂,...,ₙ be properties of graphs. A graph G is (₁,₂,...,ₙ)-partitionable if the vertex set V(G) can be partitioned into n sets, {V₁,V₂,..., Vₙ}, such that for each i = 1,2,...,n, the graph $G[V_i] ∈ _i$. We write ₁∘₂∘...∘ₙ for the property of all graphs which have a (₁,₂,...,ₙ)-partition. An additive induced-hereditary property is called reducible if there exist additive induced-hereditary properties ₁ and ₂ such that = ₁∘₂. Otherwise is called irreducible. An additive induced-hereditary property can be defined by its minimal forbidden induced subgraphs: those graphs which are not in but which satisfy that every proper induced subgraph is in . We show that every reducible additive induced-hereditary property has infinitely many minimal forbidden induced subgraphs. This result is also seen to be true for reducible additive hereditary properties.
Źródło:
Discussiones Mathematicae Graph Theory; 2001, 21, 1; 111-117
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Deficiency and Forbidden Subgraphs of Connected, Locally-Connected Graphs
Autorzy:
Li, Xihe
Wang, Ligong
Powiązania:
https://bibliotekanauki.pl/articles/32083830.pdf
Data publikacji:
2020-02-01
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
05C40
05C70
Opis:
A graph $G$ is locally-connected if the neighbourhood $ N_G (v) $ induces a connected subgraph for each vertex $v$ in $G$. For a graph $G$, the deficiency of $G$ is the number of vertices unsaturated by a maximum matching, denoted by $ \text{def} (G) $. In fact, the deficiency of a graph measures how far a maximum matching is from being perfect matching. Saito and Xiong have studied subgraphs, the absence of which forces a connected and locally-connected graph $G$ of sufficiently large order to satisfy $ \text{def} (G) \le 1 $. In this paper, we extend this result to the condition of $ \text{def} (G) \le k $, where k is a positive integer. Let $ \beta_0 = \ceil{ 1/2 (3+\sqrt{8k+17} ) } −1 $, we show that $ K_{1,2}, K_{1,3}, . . ., K_{1,β_0}, K_3 $ or \( K_2 \lor 2K_1 \) is the required forbidden subgraph. Furthermore, we obtain some similar results about 3-connected, locally-connected graphs. Key Words: deficiency, locally-connected graph, matching, forbidden subgraph.
Źródło:
Discussiones Mathematicae Graph Theory; 2020, 40, 1; 195-208
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Forbidden configurations for hypohamiltonian graphs
Autorzy:
Fabrici, I.
Madaras, T.
Timkova, M.
Powiązania:
https://bibliotekanauki.pl/articles/256013.pdf
Data publikacji:
2018
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
hypohamiltonian graph
forbidden configuration
long cycle
Opis:
A graph G is called hypohamiltonian if G is not hamiltonian, but G — x is hamiltonian for each vertex x of G. We present a list of 331 forbidden configurations which do not appear in hypohamiltonian graphs.
Źródło:
Opuscula Mathematica; 2018, 38, 3; 357-377
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Forbidden Subgraphs for Hamiltonicity of 1-Tough Graphs
Autorzy:
Li, Binlong
Broersma, Hajo J.
Zhang, Shenggui
Powiązania:
https://bibliotekanauki.pl/articles/31340596.pdf
Data publikacji:
2016-11-01
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
forbidden subgraph
1-tough graph
H-free graph
hamiltonian graph
Opis:
A graph G is said to be 1-tough if for every vertex cut S of G, the number of components of G − S does not exceed |S|. Being 1-tough is an obvious necessary condition for a graph to be hamiltonian, but it is not sufficient in general. We study the problem of characterizing all graphs H such that every 1-tough H-free graph is hamiltonian. We almost obtain a complete solution to this problem, leaving H = K1 ∪ P4 as the only open case.
Źródło:
Discussiones Mathematicae Graph Theory; 2016, 36, 4; 915-929
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Toughness, Forbidden Subgraphs, and Hamilton-Connected Graphs
Autorzy:
Zheng, Wei
Broersma, Hajo
Wang, Ligong
Powiązania:
https://bibliotekanauki.pl/articles/32361744.pdf
Data publikacji:
2022-02-01
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
toughness
forbidden subgraph
Hamilton-connected graph
Hamiltonicity
Opis:
A graph G is called Hamilton-connected if for every pair of distinct vertices {u, v} of G there exists a Hamilton path in G that connects u and v. A graph G is said to be t-tough if t·ω(G − X) ≤ |X| for all X ⊆ V (G) with ω(G − X) > 1. The toughness of G, denoted τ (G), is the maximum value of t such that G is t-tough (taking τ (Kn) = ∞ for all n ≥ 1). It is known that a Hamilton-connected graph G has toughness τ (G) > 1, but that the reverse statement does not hold in general. In this paper, we investigate all possible forbidden subgraphs H such that every H-free graph G with τ (G) > 1 is Hamilton-connected. We find that the results are completely analogous to the Hamiltonian case: every graph H such that any 1-tough H-free graph is Hamiltonian also ensures that every H-free graph with toughness larger than one is Hamilton-connected. And similarly, there is no other forbidden subgraph having this property, except possibly for the graph K1 ∪ P4 itself. We leave this as an open case.
Źródło:
Discussiones Mathematicae Graph Theory; 2022, 42, 1; 187-196
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Graph domination in distance two
Autorzy:
Bacsó, Gábor
Tálos, Attila
Tuza, Zsolt
Powiązania:
https://bibliotekanauki.pl/articles/744316.pdf
Data publikacji:
2005
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
graph
dominating set
connected domination
distance domination
forbidden induced subgraph
Opis:
Let G = (V,E) be a graph, and k ≥ 1 an integer. A subgraph D is said to be k-dominating in G if every vertex of G-D is at distance at most k from some vertex of D. For a given class of graphs, Domₖ is the set of those graphs G in which every connected induced subgraph H has some k-dominating induced subgraph D ∈ which is also connected. In our notation, Dom coincides with Dom₁. In this paper we prove that $Dom Dom _u = Dom₂ _u$ holds for $_u$ = {all connected graphs without induced $P_u$} (u ≥ 2). (In particular, ₂ = {K₁} and ₃ = {all complete graphs}.) Some negative examples are also given.
Źródło:
Discussiones Mathematicae Graph Theory; 2005, 25, 1-2; 121-128
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Dominating bipartite subgraphs in graphs
Autorzy:
Bacsó, Gábor
Michalak, Danuta
Tuza, Zsolt
Powiązania:
https://bibliotekanauki.pl/articles/744313.pdf
Data publikacji:
2005
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
dominating set
dominating subgraph
forbidden induced subgraph
bipartite graph
k-partite graph
Opis:
A graph G is hereditarily dominated by a class of connected graphs if each connected induced subgraph of G contains a dominating induced subgraph belonging to . In this paper we characterize graphs hereditarily dominated by classes of complete bipartite graphs, stars, connected bipartite graphs, and complete k-partite graphs.
Źródło:
Discussiones Mathematicae Graph Theory; 2005, 25, 1-2; 85-94
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Forbidden Pairs and (k, m)-Pancyclicity
Autorzy:
Crane, Charles Brian
Powiązania:
https://bibliotekanauki.pl/articles/31341696.pdf
Data publikacji:
2017-08-01
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
hamiltonian
pancyclic
forbidden subgraph
cycle
claw-free
Opis:
A graph G on n vertices is said to be (k,m)-pancyclic if every set of k vertices in G is contained in a cycle of length r for each r ∈ {m, m+1, . . ., n}. This property, which generalizes the notion of a vertex pancyclic graph, was defined by Faudree, Gould, Jacobson, and Lesniak in 2004. The notion of (k, m)-pancyclicity provides one way to measure the prevalence of cycles in a graph. We consider pairs of subgraphs that, when forbidden, guarantee hamiltonicity for 2-connected graphs on n ≥ 10 vertices. There are exactly ten such pairs. For each integer k ≥ 1 and each of eight such subgraph pairs {R, S}, we determine the smallest value m such that any 2-connected {R, S}-free graph on n ≥ 10 vertices is guaranteed to be (k,m)-pancyclic. Examples are provided that show the given values are best possible. Each such example we provide represents an infinite family of graphs.
Źródło:
Discussiones Mathematicae Graph Theory; 2017, 37, 3; 649-663
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Forbidden Subgraphs for Collapsible Graphs and Supereulerian Graphs
Autorzy:
Liu, Xia
Xiong, Liming
Powiązania:
https://bibliotekanauki.pl/articles/32361726.pdf
Data publikacji:
2022-05-01
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
forbidden subgraph
supereulerian
collapsible
Opis:
In this paper, we completely characterize the connected forbidden subgraphs and pairs of connected forbidden subgraphs that force a 2-edge-connected (2-connected) graph to be collapsible. In addition, the characterization of pairs of connected forbidden subgraphs that imply a 2-edge-connected graph of minimum degree at least three is supereulerian will be considered. We have given all possible forbidden pairs. In particular, we prove that every 2-edge-connected noncollapsible (or nonsupereulerian) graph of minimum degree at least three is Z3-free if and only if it is K3-free, where Zi is a graph obtained by identifying a vertex of a K3 with an end-vertex of a Pi+1.
Źródło:
Discussiones Mathematicae Graph Theory; 2022, 42, 2; 417-442
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Graphs with small additive stretch number
Autorzy:
Rautenbach, Dieter
Powiązania:
https://bibliotekanauki.pl/articles/744511.pdf
Data publikacji:
2004
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
stretch number
distance hereditary graph
forbidden induced subgraph
Opis:
The additive stretch number $s_{add}(G)$ of a graph G is the maximum difference of the lengths of a longest induced path and a shortest induced path between two vertices of G that lie in the same component of G.We prove some properties of minimal forbidden configurations for the induced-hereditary classes of graphs G with $s_{add}(G) ≤ k$ for some k ∈ N₀ = {0,1,2,...}. Furthermore, we derive characterizations of these classes for k = 1 and k = 2.
Źródło:
Discussiones Mathematicae Graph Theory; 2004, 24, 2; 291-301
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
On the 12-Representability of Induced Subgraphs of a Grid Graph
Autorzy:
Chen, Joanna N.
Kitaev, Sergey
Powiązania:
https://bibliotekanauki.pl/articles/32361728.pdf
Data publikacji:
2022-05-01
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
graph representation
12-representable graph
grid graph
forbidden subgraph
square grid graph
line grid graph
Opis:
The notion of a 12-representable graph was introduced by Jones, Kitaev, Pyatkin and Remmel in [Representing graphs via pattern avoiding words, Electron. J. Combin. 22 (2015) #P2.53]. This notion generalizes the notions of the much studied permutation graphs and co-interval graphs. It is known that any 12-representable graph is a comparability graph, and also that a tree is 12-representable if and only if it is a double caterpillar. Moreover, Jones et al. initiated the study of 12- representability of induced subgraphs of a grid graph, and asked whether it is possible to characterize such graphs. This question of Jones et al. is meant to be about induced subgraphs of a grid graph that consist of squares, which we call square grid graphs. However, an induced subgraph in a grid graph does not have to contain entire squares, and we call such graphs line grid graphs. In this paper we answer the question of Jones et al. by providing a complete characterization of 12-representable square grid graphs in terms of forbidden induced subgraphs. Moreover, we conjecture such a characterization for the line grid graphs and give a number of results towards solving this challenging conjecture. Our results are a major step in the direction of characterization of all 12-representable graphs since beyond our characterization, we also discuss relations between graph labelings and 12-representability, one of the key open questions in the area.
Źródło:
Discussiones Mathematicae Graph Theory; 2022, 42, 2; 383-403
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
The Ryjáček Closure and a Forbidden Subgraph
Autorzy:
Saito, Akira
Xiong, Liming
Powiązania:
https://bibliotekanauki.pl/articles/31340869.pdf
Data publikacji:
2016-08-01
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
closure
claw-free graph
Hamiltonian graph
perfect matching
traceable graph
Opis:
The Ryjáček closure is a powerful tool in the study of Hamiltonian properties of claw-free graphs. Because of its usefulness, we may hope to use it in the classes of graphs defined by another forbidden subgraph. In this note, we give a negative answer to this hope, and show that the claw is the only forbidden subgraph that produces non-trivial results on Hamiltonicity by the use of the Ryjáček closure.
Źródło:
Discussiones Mathematicae Graph Theory; 2016, 36, 3; 621-628
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Rainbow Vertex-Connection and Forbidden Subgraphs
Autorzy:
Li, Wenjing
Li, Xueliang
Zhang, Jingshu
Powiązania:
https://bibliotekanauki.pl/articles/31342433.pdf
Data publikacji:
2018-02-01
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
vertex-rainbow path
rainbow vertex-connection
forbidden sub-graphs
Opis:
A path in a vertex-colored graph is called vertex-rainbow if its internal vertices have pairwise distinct colors. A vertex-colored graph G is rainbow vertex-connected if for any two distinct vertices of G, there is a vertex-rainbow path connecting them. For a connected graph G, the rainbow vertex-connection number of G, denoted by rvc(G), is defined as the minimum number of colors that are required to make G rainbow vertex-connected. In this paper, we find all the families ℱ of connected graphs with |ℱ| ∈ {1, 2}, for which there is a constant kℱ such that, for every connected ℱ-free graph G, rvc(G) ≤ diam(G) + kℱ, where diam(G) is the diameter of G.
Źródło:
Discussiones Mathematicae Graph Theory; 2018, 38, 1; 143-154
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Wyświetlanie 1-15 z 27

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