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Wyświetlanie 1-15 z 26
Tytuł:
A note on joins of additive hereditary graph properties
Autorzy:
Drgas-Burchardt, Ewa
Powiązania:
https://bibliotekanauki.pl/articles/743593.pdf
Data publikacji:
2006
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
hereditary property
lattice of additive hereditary graph properties
minimal forbidden subgraph family
join in the lattice
Opis:
Let $L^a$ denote a set of additive hereditary graph properties. It is a known fact that a partially ordered set $(L^a, ⊆ )$ is a complete distributive lattice. We present results when a join of two additive hereditary graph properties in $(L^a, ⊆ )$ has a finite or infinite family of minimal forbidden subgraphs.
Źródło:
Discussiones Mathematicae Graph Theory; 2006, 26, 3; 413-418
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:
An Extension of Kotzig’s Theorem
Autorzy:
Aksenov, Valerii A.
Borodin, Oleg V.
Ivanova, Anna O.
Powiązania:
https://bibliotekanauki.pl/articles/31340608.pdf
Data publikacji:
2016-11-01
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
plane graph
normal plane map
structural property
weight
Opis:
In 1955, Kotzig proved that every 3-connected planar graph has an edge with the degree sum of its end vertices at most 13, which is tight. An edge uv is of type (i, j) if d(u) ≤ i and d(v) ≤ j. Borodin (1991) proved that every normal plane map contains an edge of one of the types (3, 10), (4, 7), or (5, 6), which is tight. Cole, Kowalik, and Škrekovski (2007) deduced from this result by Borodin that Kotzig’s bound of 13 is valid for all planar graphs with minimum degree δ at least 2 in which every d-vertex, d ≥ 12, has at most d − 11 neighbors of degree 2. We give a common extension of the three above results by proving for any integer t ≥ 1 that every plane graph with δ ≥ 2 and no d-vertex, d ≥ 11+t, having more than d − 11 neighbors of degree 2 has an edge of one of the following types: (2, 10+t), (3, 10), (4, 7), or (5, 6), where all parameters are tight.
Źródło:
Discussiones Mathematicae Graph Theory; 2016, 36, 4; 889-897
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
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:
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:
Fractional (\( \mathcal{P} , \mathcal{Q} \))-Total List Colorings of Graphs
Autorzy:
Kemnitz, Arnfried
Mihók, Peter
Voigt, Margit
Powiązania:
https://bibliotekanauki.pl/articles/30146708.pdf
Data publikacji:
2013-03-01
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
graph property
total coloring
(P,Q)-total coloring
fractional coloring
fractional (P,Q)-total chromatic number
circular coloring
circular (P,Q)-total chromatic number
list coloring
(P,Q)-total (a
b)-list colorings
Opis:
Let $ r, s \in \mathbb{N}$, $r \ge s$, and \( \mathcal{P} \) and \( \mathcal{Q} \) be two additive and hereditary graph properties. A \( (P,Q) \)-total $(r, s)$-coloring of a graph $G = (V,E)$ is a coloring of the vertices and edges of $G$ by $s$-element subsets of $ \mathbb{Z}_r$ such that for each color $i$, $0 \le i \le r − 1$, the vertices colored by subsets containing $i$ induce a subgraph of $G$ with property \( \mathcal{P} \), the edges colored by subsets containing $i$ induce a subgraph of $G$ with property \( \mathcal{Q} \), and color sets of incident vertices and edges are disjoint. The fractional \( (\mathcal{P}, \mathcal{Q})\)-total chromatic number $ \chi_{f,P,Q}^{''}(G)$ of $G$ is defined as the infimum of all ratios $r//s$ such that $G$ has a \( ( \mathcal{P}, \mathcal{Q})\)-total $(r, s)$-coloring. A \( ( \mathcal{P}, \mathcal{Q} \)-total independent set $ T = V_T \cup E_T \subseteq V \cup E$ is the union of a set $V_T$ of vertices and a set $E_T$ of edges of $G$ such that for the graphs induced by the sets $V_T$ and $E_T$ it holds that \( G[ V_T ] \in \mathcal{ P } \), \( G[ E_T ] \in \mathcal{Q} \), and $ G[ V_T ] $ and $ G[ E_T ] $ are disjoint. Let \( T_{ \mathcal{P} , \mathcal{Q} } \) be the set of all \( (\mathcal{P} ,\mathcal{Q})\)-total independent sets of $G$. Let $L(x)$ be a set of admissible colors for every element $ x \in V \cup E $. The graph $G$ is called \( (\mathcal{P} , \mathcal{Q}) \)-total $(a, b)$-list colorable if for each list assignment $L$ with $|L(x)| = a$ for all $x \in V \cup E$ it is possible to choose a subset $ C(x) \subseteq L(x)$ with $|C(x)| = b$ for all $ x \in V \cup E$ such that the set $ T_i $ which is defined by $ T_i = {x \in V \cup E : i \in C(x) } $ belongs to \( T_{ \mathcal{P},\mathcal{Q}}\) for every color $i$. The \( (\mathcal{P}, \mathcal{Q})\)- choice ratio \( \text{chr}_{\mathcal{P},\mathcal{Q}}(G)\) of $G$ is defined as the infimum of all ratios $a//b$ such that $G$ is \( (\mathcal{P},\mathcal{Q})\)-total $(a, b)$-list colorable. We give a direct proof of \( \chi_{ f,\mathcal{P},\mathcal{Q} }^{ \prime \prime } (G) = \text{chr}_{ \mathcal{P} ,\mathcal{Q} }(G)\) for all simple graphs $G$ and we present for some properties \( \mathcal{P} \) and \( \mathcal{Q} \) new bounds for the \( (\mathcal{P}, \mathcal{Q})\)-total chromatic number and for the \((\mathcal{P},\mathcal{Q})\)-choice ratio of a graph $G$.
Źródło:
Discussiones Mathematicae Graph Theory; 2013, 33, 1; 167-179
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:
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
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:
Generalized Fractional and Circular Total Colorings of Graphs
Autorzy:
Kemnitz, Arnfried
Marangio, Massimiliano
Mihók, Peter
Oravcová, Janka
Soták, Roman
Powiązania:
https://bibliotekanauki.pl/articles/31339338.pdf
Data publikacji:
2015-08-01
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
graph property
(P,Q)-total coloring
circular coloring
fractional coloring
fractional (P,Q)-total chromatic number
circular (P,Q)- total chromatic number
Opis:
Let \( \mathcal{P} \) and \( \mathcal{Q} \) be additive and hereditary graph properties, $ r, s \in \mathbb{N}$, $ r \ge s $, and $ [\mathbb{Z}_r]^s $ be the set of all s-element subsets of $\mathbb{Z}_r $. An ($r$, $s$)-fractional (\( \mathcal{P} \),\( \mathcal{Q} \))-total coloring of $G$ is an assignment $ h : V (G) \cup E(G) \rightarrow [\mathbb{Z}_r]^s $ such that for each $ i \in \mathbb{Z}_r $ the following holds: the vertices of $G$ whose color sets contain color $i$ induce a subgraph of $G$ with property \( \mathcal{P} \), edges with color sets containing color $i$ induce a subgraph of $G$ with property \( \mathcal{Q} \), and the color sets of incident vertices and edges are disjoint. If each vertex and edge of $G$ is colored with a set of $s$ consecutive elements of $ \mathbb{Z}_r $ we obtain an ($r$, $s$)-circular (\( \mathcal{P} \),\( \mathcal{Q} \))-total coloring of $G$. In this paper we present basic results on ($r$, $s$)-fractional/circular (\( \mathcal{P} \),\( \mathcal{Q} \))-total colorings. We introduce the fractional and circular (\( \mathcal{P} \),\( \mathcal{Q}\))-total chromatic number of a graph and we determine this number for complete graphs and some classes of additive and hereditary properties.
Źródło:
Discussiones Mathematicae Graph Theory; 2015, 35, 3; 517-532
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Generalized Sum List Colorings of Graphs
Autorzy:
Kemnitz, Arnfried
Marangio, Massimiliano
Voigt, Margit
Powiązania:
https://bibliotekanauki.pl/articles/31343297.pdf
Data publikacji:
2019-08-01
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
sum list coloring
sum choice number
generalized sum list coloring
additive hereditary graph property
Opis:
A (graph) property \( \mathcal{P} \) is a class of simple finite graphs closed under isomorphisms. In this paper we consider generalizations of sum list colorings of graphs with respect to properties \( \mathcal{P} \). If to each vertex $v$ of a graph $G$ a list $L(v)$ of colors is assigned, then in an \( (L, \mathcal{P} ) \)-coloring of $G$ every vertex obtains a color from its list and the subgraphs of $G$ induced by vertices of the same color are always in \( \mathcal{P} \). The \( \mathcal{P} \)-sum choice number \( X_{sc}^\mathcal{P} (G) \) of $G$ is the minimum of the sum of all list sizes such that, for any assignment $L$ of lists of colors with the given sizes, there is always an \( (L, \mathcal{P} ) \)-coloring of $G$. We state some basic results on monotonicity, give upper bounds on the \( \mathcal{P} \)-sum choice number of arbitrary graphs for several properties, and determine the \( \mathcal{P} \)-sum choice number of specific classes of graphs, namely, of all complete graphs, stars, paths, cycles, and all graphs of order at most 4.
Źródło:
Discussiones Mathematicae Graph Theory; 2019, 39, 3; 689-703
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:
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:
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:
On the lattice of additive hereditary properties of finite graphs
Autorzy:
Jakubík, Ján
Powiązania:
https://bibliotekanauki.pl/articles/729033.pdf
Data publikacji:
2002
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
Lattice
complete distributivity
finite graph
additive hereditary property
generalized Jordan-Dedekind condition
Opis:
In this paper it is proved that the lattice of additive hereditary properties of finite graphs is completely distributive and that it does not satisfy the Jordan-Dedekind condition for infinite chains.
Źródło:
Discussiones Mathematicae - General Algebra and Applications; 2002, 22, 1; 73-86
1509-9415
Pojawia się w:
Discussiones Mathematicae - General Algebra and Applications
Dostawca treści:
Biblioteka Nauki
Artykuł
Wyświetlanie 1-15 z 26

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