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Wyświetlanie 1-15 z 18
Tytuł:
Hamiltonicity and Generalised Total Colourings of Planar Graphs
Autorzy:
Borowiecki, Mieczysław
Broere, Izak
Powiązania:
https://bibliotekanauki.pl/articles/31341094.pdf
Data publikacji:
2016-05-01
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
even planar triangulation
total colouring
Hamilton cycle
hereditary property
Opis:
The total generalised colourings considered in this paper are colourings of graphs such that the vertices and edges of the graph which receive the same colour induce subgraphs from two prescribed hereditary graph properties while incident elements receive different colours. The associated total chromatic number is the least number of colours with which this is possible. We study such colourings for sets of planar graphs and determine, in particular, upper bounds for these chromatic numbers for proper colourings of the vertices while the monochromatic edge sets are allowed to be forests. We also prove that if an even planar triangulation has a Hamilton cycle H for which there is no cycle among the edges inside H, then such a graph needs at most four colours for a total colouring as described above. The paper is concluded with some conjectures and open problems.
Źródło:
Discussiones Mathematicae Graph Theory; 2016, 36, 2; 243-257
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Hereditarnia
Autorzy:
Broere, Izak
Mihók, Peter
Powiązania:
https://bibliotekanauki.pl/articles/31231995.pdf
Data publikacji:
2013-03-01
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Źródło:
Discussiones Mathematicae Graph Theory; 2013, 33, 1; 7-7
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Universality for and in Induced-Hereditary Graph Properties
Autorzy:
Broere, Izak
Heidema, Johannes
Powiązania:
https://bibliotekanauki.pl/articles/30146860.pdf
Data publikacji:
2013-03-01
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
countable graph
universal graph
induced-hereditary property
Opis:
The well-known Rado graph $R$ is universal in the set of all countable graphs \( \mathcal{I} \), since every countable graph is an induced subgraph of $R$. We study universality in \( \mathcal{I} \) and, using $R$, show the existence of $2^{\aleph_0}$ pairwise non-isomorphic graphs which are universal in \( \mathcal{I} \) and denumerably many other universal graphs in \( \mathcal{I} \) with prescribed attributes. Then we contrast universality for and universality in induced-hereditary properties of graphs and show that the overwhelming majority of induced-hereditary properties contain no universal graphs. This is made precise by showing that there are $ 2^{2^{\aleph_0 } }$ properties in the lattice $ \mathbb{K}_\le $ of induced-hereditary properties of which only at most $ 2^{\aleph_0} $ contain universal graphs. In a final section we discuss the outlook on future work; in particular the question of characterizing those induced-hereditary properties for which there is a universal graph in the property.
Źródło:
Discussiones Mathematicae Graph Theory; 2013, 33, 1; 33-47
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:
Minimal reducible bounds for hom-properties of graphs
Autorzy:
Berger, Amelie
Broere, Izak
Powiązania:
https://bibliotekanauki.pl/articles/744144.pdf
Data publikacji:
1999
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
graph homomorphisms
minimal reducible bounds
additive hereditary graph property
Opis:
Let H be a fixed finite graph and let → H be a hom-property, i.e. the set of all graphs admitting a homomorphism into H. We extend the definition of → H to include certain infinite graphs H and then describe the minimal reducible bounds for → H in the lattice of additive hereditary properties and in the lattice of hereditary properties.
Źródło:
Discussiones Mathematicae Graph Theory; 1999, 19, 2; 143-158
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Generalized chromatic numbers and additive hereditary properties of graphs
Autorzy:
Broere, Izak
Dorfling, Samantha
Jonck, Elizabeth
Powiązania:
https://bibliotekanauki.pl/articles/743358.pdf
Data publikacji:
2002
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
property of graphs
additive
hereditary
generalized chromatic number
Opis:
An additive hereditary property of graphs is a class of simple graphs which is closed under unions, subgraphs and isomorphisms. Let and be additive hereditary properties of graphs. The generalized chromatic number $χ_{}()$ is defined as follows: $χ_{}() = n$ iff ⊆ ⁿ but $ ⊊ ^{n-1}$. We investigate the generalized chromatic numbers of the well-known properties of graphs ₖ, ₖ, ₖ, ₖ and ₖ.
Źródło:
Discussiones Mathematicae Graph Theory; 2002, 22, 2; 259-270
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Note on partitions of planar graphs
Autorzy:
Broere, Izak
Wilson, Bonita
Bucko, Jozef
Powiązania:
https://bibliotekanauki.pl/articles/744336.pdf
Data publikacji:
2005
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
planar graph
hereditary property of graphs
forest and triangle-free graph
Opis:
Chartrand and Kronk in 1969 showed that there are planar graphs whose vertices cannot be partitioned into two parts inducing acyclic subgraphs. In this note we show that the same is true even in the case when one of the partition classes is required to be triangle-free only.
Źródło:
Discussiones Mathematicae Graph Theory; 2005, 25, 1-2; 211-215
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Universality in Graph Properties with Degree Restrictions
Autorzy:
Broere, Izak
Heidema, Johannes
Mihók, Peter
Powiązania:
https://bibliotekanauki.pl/articles/30146518.pdf
Data publikacji:
2013-07-01
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
countable graph
universal graph
induced-hereditary
k-degenerate graph
graph with colouring number at most k + 1
graph property with assignment
Opis:
Rado constructed a (simple) denumerable graph R with the positive integers as vertex set with the following edges: For given m and n with m < n, m is adjacent to n if n has a 1 in the m’th position of its binary expansion. It is well known that R is a universal graph in the set ℐc of all countable graphs (since every graph in ℐc is isomorphic to an induced subgraph of R). A brief overview of known universality results for some induced-hereditary subsets of ℐc is provided. We then construct a k-degenerate graph which is universal for the induced-hereditary property of finite k-degenerate graphs. In order to attempt the corresponding problem for the property of countable graphs with colouring number at most k + 1, the notion of a property with assignment is introduced and studied. Using this notion, we are able to construct a universal graph in this graph property and investigate its attributes.
Źródło:
Discussiones Mathematicae Graph Theory; 2013, 33, 3; 477-492
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Congruences and Hoehnke Radicals on Graphs
Autorzy:
Broere, Izak
Heidema, Johannes
Veldsman, Stefan
Powiązania:
https://bibliotekanauki.pl/articles/31348128.pdf
Data publikacji:
2020-11-01
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
congruences and quotients of graphs
Hoehnke radicals of graphs
connectednesses and disconnectednesses of graphs
Kurosh-Amitsur radicals of graphs
subdirect representations of graphs
Opis:
We motivate, introduce, and study radicals on classes of graphs. This concept, and the theory which is developed, imitates the original notion of a Hoehnke radical in universal algebra using congruences. It is shown how this approach ties in with the existing theory of connectednesses and disconnectednesses (= Kurosh-Amitsur radical theory).
Źródło:
Discussiones Mathematicae Graph Theory; 2020, 40, 4; 1067-1084
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:
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:
Maximal graphs with respect to hereditary properties
Autorzy:
Broere, Izak
Frick, Marietjie
Semanišin, Gabriel
Powiązania:
https://bibliotekanauki.pl/articles/972029.pdf
Data publikacji:
1997
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
hereditary property of graphs
maximal graphs
vertex partition
Opis:
A property of graphs is a non-empty set of graphs. A property P is called hereditary if every subgraph of any graph with property P also has property P. Let P₁, ...,Pₙ be properties of graphs. We say that a graph G has property P₁∘...∘Pₙ if the vertex set of G can be partitioned into n sets V₁, ...,Vₙ such that the subgraph of G induced by V_i has property $P_i$; i = 1,..., n. A hereditary property R is said to be reducible if there exist two hereditary properties P₁ and P₂ such that R = P₁∘P₂. If P is a hereditary property, then a graph G is called P- maximal if G has property P but G+e does not have property P for every e ∈ E([G̅]). We present some general results on maximal graphs and also investigate P-maximal graphs for various specific choices of P, including reducible hereditary properties.
Źródło:
Discussiones Mathematicae Graph Theory; 1997, 17, 1; 51-66
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Criteria for of the existence of uniquely partitionable graphs with respect to additive induced-hereditary properties
Autorzy:
Broere, Izak
Bucko, Jozef
Mihók, Peter
Powiązania:
https://bibliotekanauki.pl/articles/743535.pdf
Data publikacji:
2002
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
induced-hereditary properties
reducibility
divisibility
uniquely partitionable graphs.
Opis:
Let ₁,₂,...,ₙ be graph properties, a graph G is said to be uniquely (₁,₂, ...,ₙ)-partitionable if there is exactly one (unordered) partition {V₁,V₂,...,Vₙ} of V(G) such that $G[V_i] ∈ _i$ for i = 1,2,...,n. We prove that for additive and induced-hereditary properties uniquely (₁,₂,...,ₙ)-partitionable graphs exist if and only if $_i$ and $_j$ are either coprime or equal irreducible properties of graphs for every i ≠ j, i,j ∈ {1,2,...,n}.
Źródło:
Discussiones Mathematicae Graph Theory; 2002, 22, 1; 31-37
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
Wyświetlanie 1-15 z 18

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