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Wyświetlanie 1-15 z 18
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:
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:
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:
Unique factorization theorem
Autorzy:
Mihók, Peter
Powiązania:
https://bibliotekanauki.pl/articles/743745.pdf
Data publikacji:
2000
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
induced-hereditary
additive property of graphs
reducible property of graphs
unique factorization
uniquely partitionable graphs
generating sets
Opis:
A property of graphs is any class of graphs closed under isomorphism. A property of graphs is induced-hereditary and additive if it is closed under taking induced subgraphs and disjoint unions of graphs, respectively. Let ₁,₂, ...,ₙ be properties of graphs. A graph G is (₁,₂,...,ₙ)-partitionable (G has property ₁ º₂ º... ºₙ) if the vertex set V(G) of G can be partitioned into n sets V₁,V₂,..., Vₙ such that the subgraph $G[V_i]$ of G induced by V_i belongs to $_i$; i = 1,2,...,n. A property is said to be reducible if there exist properties ₁ and ₂ such that = ₁ º₂; otherwise the property is irreducible. We prove that every additive and induced-hereditary property is uniquely factorizable into irreducible factors. Moreover the unique factorization implies the existence of uniquely (₁,₂, ...,ₙ)-partitionable graphs for any irreducible properties ₁,₂, ...,ₙ.
Źródło:
Discussiones Mathematicae Graph Theory; 2000, 20, 1; 143-154
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 order of uniquely partitionable graphs
Autorzy:
Broere, Izak
Frick, Marietjie
Mihók, Peter
Powiązania:
https://bibliotekanauki.pl/articles/972025.pdf
Data publikacji:
1997
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
hereditary property of graphs
uniquely partitionable graphs
Opis:
Let ₁,...,ₙ be properties of graphs. A (₁,...,ₙ)-partition of a graph G is a partition {V₁,...,Vₙ} of V(G) such that, for each i = 1,...,n, the subgraph of G induced by $V_i$ has property $_i$. If a graph G has a unique (₁,...,ₙ)-partition we say it is uniquely (₁,...,ₙ)-partitionable. We establish best lower bounds for the order of uniquely (₁,...,ₙ)-partitionable graphs, for various choices of ₁,...,ₙ.
Źródło:
Discussiones Mathematicae Graph Theory; 1997, 17, 1; 115-125
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Prime ideals in the lattice of additive induced-hereditary graph properties
Autorzy:
Berger, Amelie
Mihók, Peter
Powiązania:
https://bibliotekanauki.pl/articles/743387.pdf
Data publikacji:
2003
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
hereditary graph property
prime ideal
distributive lattice
induced subgraphs
Opis:
An additive induced-hereditary property of graphs is any class of finite simple graphs which is closed under isomorphisms, disjoint unions and induced subgraphs. The set of all additive induced-hereditary properties of graphs, partially ordered by set inclusion, forms a completely distributive lattice. We introduce the notion of the join-decomposability number of a property and then we prove that the prime ideals of the lattice of all additive induced-hereditary properties are divided into two groups, determined either by a set of excluded join-irreducible properties or determined by a set of excluded properties with infinite join-decomposability number. We provide non-trivial examples of each type.
Źródło:
Discussiones Mathematicae Graph Theory; 2003, 23, 1; 117-127
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Uniquely partitionable graphs
Autorzy:
Bucko, Jozef
Frick, Marietjie
Mihók, Peter
Vasky, Roman
Powiązania:
https://bibliotekanauki.pl/articles/972032.pdf
Data publikacji:
1997
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
hereditary property of graphs
additivity
reducibility
vertex partition
Opis:
Let ₁,...,ₙ be properties of graphs. A (₁,...,ₙ)-partition of a graph G is a partition of the vertex set V(G) into subsets V₁, ...,Vₙ such that the subgraph $G[V_i]$ induced by $V_i$ has property $_i$; i = 1,...,n. A graph G is said to be uniquely (₁, ...,ₙ)-partitionable if G has exactly one (₁,...,ₙ)-partition. A property is called hereditary if every subgraph of every graph with property also has property . If every graph that is a disjoint union of two graphs that have property also has property , then we say that is additive. A property is called degenerate if there exists a bipartite graph that does not have property . In this paper, we prove that if ₁,..., ₙ are degenerate, additive, hereditary properties of graphs, then there exists a uniquely (₁,...,ₙ)-partitionable graph.
Źródło:
Discussiones Mathematicae Graph Theory; 1997, 17, 1; 103-113
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Remarks on the existence of uniquely partitionable planar graphs
Autorzy:
Borowiecki, Mieczysław
Mihók, Peter
Tuza, Zsolt
Voigt, M.
Powiązania:
https://bibliotekanauki.pl/articles/744146.pdf
Data publikacji:
1999
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
property of graphs
additive
hereditary
vertex partition
uniquely partitionable graphs
Opis:
We consider the problem of the existence of uniquely partitionable planar graphs. We survey some recent results and we prove the nonexistence of uniquely (₁,₁)-partitionable planar graphs with respect to the property ₁ "to be a forest".
Źródło:
Discussiones Mathematicae Graph Theory; 1999, 19, 2; 159-166
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
On generalized list colourings of graphs
Autorzy:
Borowiecki, Mieczysław
Broere, Izak
Mihók, Peter
Powiązania:
https://bibliotekanauki.pl/articles/972024.pdf
Data publikacji:
1997
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
hereditary property of graphs
list colouring
vertex partition number
Opis:
Vizing [15] and Erdős et al. [8] independently introduce the idea of considering list-colouring and k-choosability. In the both papers the choosability version of Brooks' theorem [4] was proved but the choosability version of Gallai's theorem [9] was proved independently by Thomassen [14] and by Kostochka et al. [11]. In [3] some extensions of these two basic theorems to (,k)-choosability have been proved.
In this paper we prove some extensions of the well-known bounds for the -chromatic number to the (,k)-choice number and then an extension of Brooks' theorem.
Źródło:
Discussiones Mathematicae Graph Theory; 1997, 17, 1; 127-132
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Generalized list colourings of graphs
Autorzy:
Borowiecki, Mieczysław
Drgas-Burchardt, Ewa
Mihók, Peter
Powiązania:
https://bibliotekanauki.pl/articles/972045.pdf
Data publikacji:
1995
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
hereditary property of graphs
list colouring
vertex partition number
Opis:
We prove: (1) that $ch_P(G) - χ_P(G)$ can be arbitrarily large, where $ch_P(G)$ and $χ_P(G)$ are P-choice and P-chromatic numbers, respectively, (2) the (P,L)-colouring version of Brooks' and Gallai's theorems.
Źródło:
Discussiones Mathematicae Graph Theory; 1995, 15, 2; 185-193
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
On infinite uniquely partitionable graphs and graph properties of finite character
Autorzy:
Bucko, Jozef
Mihók, Peter
Powiązania:
https://bibliotekanauki.pl/articles/743160.pdf
Data publikacji:
2009
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
graph property of finite character
reducibility
uniquely partitionable graphs
weakly universal graph
Opis:
A graph property is any nonempty isomorphism-closed class of simple (finite or infinite) graphs. A graph property is of finite character if a graph G has a property if and only if every finite induced subgraph of G has a property . Let ₁,₂,...,ₙ be graph properties of finite character, a graph G is said to be (uniquely) (₁, ₂, ...,ₙ)-partitionable if there is an (exactly one) partition {V₁, V₂, ..., Vₙ} of V(G) such that $G[V_i] ∈ _i$ for i = 1,2,...,n. Let us denote by ℜ = ₁ ∘ ₂ ∘ ... ∘ ₙ the class of all (₁,₂,...,ₙ)-partitionable graphs. A property ℜ = ₁ ∘ ₂ ∘ ... ∘ ₙ, n ≥ 2 is said to be reducible. We prove that any reducible additive graph property ℜ of finite character has a uniquely (₁, ₂, ...,ₙ)-partitionable countable generating graph. We also prove that for a reducible additive hereditary graph property ℜ of finite character there exists a weakly universal countable graph if and only if each property $_i$ has a weakly universal graph.
Źródło:
Discussiones Mathematicae Graph Theory; 2009, 29, 2; 241-251
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Generalized circular colouring of graphs
Autorzy:
Mihók, Peter
Oravcová, Janka
Soták, Roman
Powiązania:
https://bibliotekanauki.pl/articles/743910.pdf
Data publikacji:
2011
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
graph property
P-colouring
circular colouring
strong circular P-chromatic number
Opis:
Let P be a graph property and r,s ∈ N, r ≥ s. A strong circular (P,r,s)-colouring of a graph G is an assignment f:V(G) → {0,1,...,r-1}, such that the edges uv ∈ E(G) satisfying |f(u)-f(v)| < s or |f(u)-f(v)| > r - s, induce a subgraph of G with the propery P. In this paper we present some basic results on strong circular (P,r,s)-colourings. We introduce the strong circular P-chromatic number of a graph and we determine the strong circular P-chromatic number of complete graphs for additive and hereditary graph properties.
Źródło:
Discussiones Mathematicae Graph Theory; 2011, 31, 2; 345-356
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Wyświetlanie 1-15 z 18

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