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Wyświetlanie 1-15 z 55
Tytuł:
Factorizations of properties of graphs
Autorzy:
Broere, Izak
Teboho Moagi, Samuel
Mihók, Peter
Vasky, Roman
Powiązania:
https://bibliotekanauki.pl/articles/744148.pdf
Data publikacji:
1999
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
factorization
property of graphs
irreducible property
reducible property
lattice of properties of graphs
Opis:
A property of graphs is any isomorphism closed class of simple graphs. For given properties of graphs ₁,₂,...,ₙ a vertex (₁, ₂, ...,ₙ)-partition of a graph G is a partition {V₁,V₂,...,Vₙ} of V(G) such that for each i = 1,2,...,n the induced subgraph $G[V_i]$ has property $_i$. The class of all graphs having a vertex (₁, ₂, ...,ₙ)-partition is denoted by ₁∘₂∘...∘ₙ. A property is said to be reducible with respect to a lattice of properties of graphs if there are n ≥ 2 properties ₁,₂,...,ₙ ∈ such that = ₁∘₂∘...∘ₙ; otherwise is irreducible in . We study the structure of different lattices of properties of graphs and we prove that in these lattices every reducible property of graphs has a finite factorization into irreducible properties.
Źródło:
Discussiones Mathematicae Graph Theory; 1999, 19, 2; 167-174
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
On the tree graph of a connected graph
Autorzy:
Figueroa, Ana
Rivera-Campo, Eduardo
Powiązania:
https://bibliotekanauki.pl/articles/743083.pdf
Data publikacji:
2008
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
tree graph
property Δ*
property Δ⁺
Opis:
Let G be a graph and C be a set of cycles of G. The tree graph of G defined by C, is the graph T(G,C) that has one vertex for each spanning tree of G, in which two trees T and T' are adjacent if their symmetric difference consists of two edges and the unique cycle contained in T ∪ T' is an element of C. We give a necessary and sufficient condition for this graph to be connected for the case where every edge of G belongs to at most two cycles in C.
Źródło:
Discussiones Mathematicae Graph Theory; 2008, 28, 3; 501-510
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:
Generalized colorings and avoidable orientations
Autorzy:
Szigeti, Jenő
Tuza, Zsolt
Powiązania:
https://bibliotekanauki.pl/articles/971967.pdf
Data publikacji:
1997
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
hereditary property
graph coloring
Opis:
Gallai and Roy proved that a graph is k-colorable if and only if it has an orientation without directed paths of length k. We initiate the study of analogous characterizations for the existence of generalized graph colorings, where each color class induces a subgraph satisfying a given (hereditary) property. It is shown that a graph is partitionable into at most k independent sets and one induced matching if and only if it admits an orientation containing no subdigraph from a family of k+3 directed graphs.
Źródło:
Discussiones Mathematicae Graph Theory; 1997, 17, 1; 137-145
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
On the completeness of decomposable properties of graphs
Autorzy:
Hałuszczak, Mariusz
Vateha, Pavol
Powiązania:
https://bibliotekanauki.pl/articles/744156.pdf
Data publikacji:
1999
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
decomposition
hereditary property
completeness
Opis:
Let ₁,₂ be additive hereditary properties of graphs. A (₁,₂)-decomposition of a graph G is a partition of E(G) into sets E₁, E₂ such that induced subgraph $G[E_i]$ has the property $_i$, i = 1,2. Let us define a property ₁⊕₂ by {G: G has a (₁,₂)-decomposition}.
A property D is said to be decomposable if there exists nontrivial additive hereditary properties ₁, ₂ such that D = ₁⊕₂. In this paper we determine the completeness of some decomposable properties and we characterize the decomposable properties of completeness 2.
Źródło:
Discussiones Mathematicae Graph Theory; 1999, 19, 2; 229-236
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:
Graphs maximal with respect to hom-properties
Autorzy:
Kratochvíl, Jan
Mihók, Peter
Semanišin, Gabriel
Powiązania:
https://bibliotekanauki.pl/articles/971980.pdf
Data publikacji:
1997
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
hom-property of graphs
hereditary property of graphs
maximal graphs
Opis:
For a simple graph H, →H denotes the class of all graphs that admit homomorphisms to H (such classes of graphs are called hom-properties). We investigate hom-properties from the point of view of the lattice of hereditary properties. In particular, we are interested in characterization of maximal graphs belonging to →H. We also provide a description of graphs maximal with respect to reducible hom-properties and determine the maximum number of edges of graphs belonging to →H.
Źródło:
Discussiones Mathematicae Graph Theory; 1997, 17, 1; 77-88
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
A survey of hereditary properties of graphs
Autorzy:
Borowiecki, Mieczysław
Broere, Izak
Frick, Marietjie
Mihók, Peter
Semanišin, Gabriel
Powiązania:
https://bibliotekanauki.pl/articles/971986.pdf
Data publikacji:
1997
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
hereditary property of graphs
vertex partition
reducible property
graph invariants
complexity
Opis:
In this paper we survey results and open problems on the structure of additive and hereditary properties of graphs. The important role of vertex partition problems, in particular the existence of uniquely partitionable graphs and reducible properties of graphs in this structure is emphasized. Many related topics, including questions on the complexity of related problems, are investigated.
Źródło:
Discussiones Mathematicae Graph Theory; 1997, 17, 1; 5-50
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Fractional -Edge-Coloring of Graphs
Autorzy:
Czap, Július
Mihók, Peter
Powiązania:
https://bibliotekanauki.pl/articles/30146484.pdf
Data publikacji:
2013-07-01
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
fractional coloring
graph property
Opis:
An additive hereditary property of graphs is a class of simple graphs which is closed under unions, subgraphs and isomorphism. Let be an additive hereditary property of graphs. A -edge-coloring of a simple graph is an edge coloring in which the edges colored with the same color induce a subgraph of property . In this paper we present some results on fractional -edge-colorings. We determine the fractional -edge chromatic number for matroidal properties of graphs.
Źródło:
Discussiones Mathematicae Graph Theory; 2013, 33, 3; 509-519
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Hereditary domination and independence parameters
Autorzy:
Goddard, Wayne
Haynes, Teresa
Knisley, Debra
Powiązania:
https://bibliotekanauki.pl/articles/743912.pdf
Data publikacji:
2004
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
domination
hereditary property
independence
Opis:
For a graphical property P and a graph G, we say that a subset S of the vertices of G is a P-set if the subgraph induced by S has the property P. Then the P-domination number of G is the minimum cardinality of a dominating P-set and the P-independence number the maximum cardinality of a P-set. We show that several properties of domination, independent domination and acyclic domination hold for arbitrary properties P that are closed under disjoint unions and subgraphs.
Źródło:
Discussiones Mathematicae Graph Theory; 2004, 24, 2; 239-248
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Gallais innequality for critical graphs of reducible hereditary properties
Autorzy:
Mihók, Peter
Skrekovski, Riste
Powiązania:
https://bibliotekanauki.pl/articles/743466.pdf
Data publikacji:
2001
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
additive induced-hereditary property of graphs
reducible property of graphs
critical graph
Gallai's Theorem
Opis:
In this paper Gallai's inequality on the number of edges in critical graphs is generalized for reducible additive induced-hereditary properties of graphs in the following way. Let $₁,₂,...,ₖ$ (k ≥ 2) be additive induced-hereditary properties, $ = ₁ ∘ ₂ ∘ ... ∘ₖ$ and $δ = ∑_{i=1}^k δ(_i)$. Suppose that G is an -critical graph with n vertices and m edges. Then 2m ≥ δn + (δ-2)/(δ²+2δ-2)*n + (2δ)/(δ²+2δ-2) unless = ² or $G = K_{δ+1}$. The generalization of Gallai's inequality for -choice critical graphs is also presented.
Źródło:
Discussiones Mathematicae Graph Theory; 2001, 21, 2; 167-177
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Reducible properties of graphs
Autorzy:
Mihók, P.
Semanišin, G.
Powiązania:
https://bibliotekanauki.pl/articles/972021.pdf
Data publikacji:
1995
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
hereditary property of graphs
additivity
reducibility
Opis:
Let L be the set of all hereditary and additive properties of graphs. For P₁, P₂ ∈ L, the reducible property R = P₁∘P₂ is defined as follows: G ∈ R if and only if there is a partition V(G) = V₁∪ V₂ of the vertex set of G such that $⟨V₁⟩_G ∈ P₁$ and $⟨V₂⟩_G ∈ P₂$. The aim of this paper is to investigate the structure of the reducible properties of graphs with emphasis on the uniqueness of the decomposition of a reducible property into irreducible ones.
Źródło:
Discussiones Mathematicae Graph Theory; 1995, 15, 1; 11-18
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
On partitions of hereditary properties of graphs
Autorzy:
Borowiecki, Mieczysław
Fiedorowicz, Anna
Powiązania:
https://bibliotekanauki.pl/articles/743575.pdf
Data publikacji:
2006
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
hereditary property
acyclic colouring
Ramsey class
Opis:
In this paper a concept -Ramsey Class of graphs is introduced, where is a class of bipartite graphs. It is a generalization of well-known concept of Ramsey Class of graphs. Some -Ramsey Classes of graphs are presented (Theorem 1 and 2). We proved that ₂, the class of all outerplanar graphs, is not ₁-Ramsey Class (Theorem 3). This results leads us to the concept of acyclic reducible bounds for a hereditary property . For ₂ we found two bounds (Theorem 4). An improvement, in some sense, of that in Theorem is given.
Źródło:
Discussiones Mathematicae Graph Theory; 2006, 26, 3; 377-387
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
The Armendariz Graph of a Ring
Autorzy:
Abdioğlu, Cihat
Çelikel, Ece Yetkin
Das, Angsuman
Powiązania:
https://bibliotekanauki.pl/articles/52678678.pdf
Data publikacji:
2018-12-01
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
Armendariz property
diameter
girth
zero-divisor graph
Opis:
In this paper we initiate the study of Armendariz graph of a commutative ring $R$ and investigate the basic properties of this graph such as diameter, girth, domination number, etc. The Armendariz graph of a ring $R$, denoted by $A(R)$, is an undirected graph with nonzero zero-divisors of $R[x]$ (i.e., $Z(R[x])^{\ast}$) as the vertex set, and two distinct vertices \(f(x)=∑_{i=0}^na_ix^i\) and \(g(x)=∑_{j=0}^mb_jx^j\) are adjacent if and only if $a_ib_j = 0$, for all $i$, $j$. It is shown that $A(R)$, a subgraph of $Γ(R[x])$, the zero divisor graph of the polynomial ring $R[x]$, have many graph properties in common with $Γ(R[x])$.
Źródło:
Discussiones Mathematicae - General Algebra and Applications; 2018, 38, 2; 189-196
1509-9415
Pojawia się w:
Discussiones Mathematicae - General Algebra and Applications
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Degree sequences of digraphs with highly irregular property
Autorzy:
Majcher, Zofia
Michael, Jerzy
Powiązania:
https://bibliotekanauki.pl/articles/972042.pdf
Data publikacji:
1998
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
digraph
degree sequence
highly irregular property
Opis:
A digraph such that for each its vertex, vertices of the out-neighbourhood have different in-degrees and vertices of the in-neighbourhood have different out-degrees, will be called an HI-digraph. In this paper, we give a characterization of sequences of pairs of out- and in-degrees of HI-digraphs.
Źródło:
Discussiones Mathematicae Graph Theory; 1998, 18, 1; 49-61
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Wyświetlanie 1-15 z 55

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