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Prace opublikowane w tym czasopiśmie
Filtry
wszystkich: 28
Katalog Czasopism
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Total outer-connected domination in trees
PublikacjaW pracy przedstawiono dolne ograniczenie na liczbę dominowania totalnego zewnętrznie spójnego w grafach oraz scharakteryzowano wszystkie drzewa osiągające to ograniczenie.
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Parity vertex colouring of graphs
PublikacjaA parity path in a vertex colouring of a graph is a path along which each colour is used an even number of times. Let Xp(G) be the least number of colours in a proper vertex colouring of G having no parity path. It is proved that for any graph G we have the following tight bounds X(G) <= Xp(G) <=|V(G)|− a(G)+1, where X(G) and a(G) are the chromatic number and the independence number of G, respectively. The bounds are improved for...
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Domination subdivision and domination multisubdivision numbers of graphs
PublikacjaThe domination subdivision number sd(G) of a graph G is the minimum number of edges that must be subdivided (where an edge can be subdivided at most once) in order to increase the domination number of G. It has been shown [10] that sd(T)<=3 for any tree T. We prove that the decision problem of the domination subdivision number is NP-complete even for bipartite graphs. For this reason we define the domination multisubdivision number...
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TOTAL DOMINATION MULTISUBDIVISION NUMBER OF A GRAPH
PublikacjaThe domination multisubdivision number of a nonempty graph G was defined in [3] as the minimum positive integer k such that there exists an edge which must be subdivided k times to increase the domination number of G. Similarly we define the total domination multisubdivision number msd_t (G) of a graph G and we show that for any connected graph G of order at least two, msd_t (G) ≤ 3. We show that for trees the total domination...
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Trees with equal restrained domination and total restrained domination numbers
PublikacjaW publikacji scharakteryzowano wszystkie drzewa, w których liczby dominowania powściągniętego oraz podwójnie totalnego są sobie równe.
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Equitable coloring of corona multiproducts of graphs
PublikacjaWe give some results regarding the equitable chromatic number for l-corona product of two graphs: G and H, where G is an equitably 3- or 4-colorable graph and H is an r-partite graph, a cycle or a complete graph. Our proofs lead to polynomial algorithms for equitable coloring of such graph products provided that there is given an equitable coloring of G.
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On incidence coloring of coloring of complete multipartite and semicubic bipartite graphs
PublikacjaIn the paper, we show that the incidence chromatic number of a complete k-partite graph is at most ∆+2 (i.e., proving the incidence coloring conjecture for these graphs) and it is equal to ∆+1 if and only if the smallest part has only one vertex.
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Convex universal fixers
PublikacjaPraca dotyczy dominowania wypukłego w grafach pryzmowych.
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Efficient list cost coloring of vertices and/or edges of bounded cyclicity graphs
Publikacja -
Total domination in versus paired-domination in regular graphs
PublikacjaA subset S of vertices of a graph G is a dominating set of G if every vertex not in S has a neighbor in S, while S is a total dominating set of G if every vertex has a neighbor in S. If S is a dominating set with the additional property that the subgraph induced by S contains a perfect matching, then S is a paired-dominating set. The domination number, denoted γ(G), is the minimum cardinality of a dominating set of G, while the...
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Some variations of perfect graphs
PublikacjaWe consider (ψk−γk−1)-perfect graphs, i.e., graphs G for which ψk(H) =γk−1(H) for any induced subgraph H of G, where ψk and γk−1 are the k -path vertex cover number and the distance (k−1)-domination number, respectively. We study (ψk−γk−1)-perfect paths, cycles and complete graphs for k≥2. Moreover, we provide a complete characterisation of (ψ2−γ1)-perfect graphs describing the set of its forbidden induced subgraphs and providing...
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On-line P-coloring of graphs
PublikacjaFor a given induced hereditary property P, a P-coloring of a graph G is an assignment of one color to each vertex such that the subgraphs induced by each of the color classes have property P. We consider the effectiveness of on-line P-coloring algorithms and give the generalizations and extensions of selected results known for on-line proper coloring algorithms. We prove a linear lower bound for the performance guarantee function...
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Interval incidence coloring of subcubic graphs
PublikacjaIn this paper we study the problem of interval incidence coloring of subcubic graphs. In [14] the authors proved that the interval incidence 4-coloring problem is polynomially solvable and the interval incidence 5-coloring problem is N P-complete, and they asked if χii(G) ≤ 2∆(G) holds for an arbitrary graph G. In this paper, we prove that an interval incidence 6-coloring always exists for any subcubic graph G with ∆(G) = 3.
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Block graphs with large paired domination multisubdivision number
PublikacjaThe paired domination multisubdivision number of a nonempty graph G, denoted by msdpr(G), is the smallest positive integer k such that there exists an edge which must be subdivided k times to increase the paired domination number of G. It is known that msdpr(G) ≤ 4 for all graphs G. We characterize block graphs with msdpr(G) = 4.
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Domination numbers in graphs with removed edge or set of edges
PublikacjaW artykule przedstawiony jest wpływ usuwania krawędzi lub zbioru krawędzi na liczby dominowania spójnego i słabo spójnego.
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A note on polynomial algorithm for cost coloring of bipartite graphs with Δ ≤ 4
PublikacjaIn the note we consider vertex coloring of a graph in which each color has an associated cost which is incurred each time the color is assigned to a vertex. The cost of coloring is the sum of costs incurred at each vertex. We show that the minimum cost coloring problem for n-vertex bipartite graph of degree ∆≤4 can be solved in O(n^2) time. This extends Jansen’s result [K.Jansen,The optimum cost chromatic partition problem, in:...
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Graph classes generated by Mycielskians
PublikacjaIn this paper we use the classical notion of weak Mycielskian M'(G) of a graph G and the following sequence: M'_{0}(G) =G, M'_{1}(G)=M'(G), and M'_{n}(G)=M'(M'_{n−1}(G)), to show that if G is a complete graph oforder p, then the above sequence is a generator of the class of p-colorable graphs. Similarly, using Mycielskian M(G) we show that analogously defined sequence is a generator of the class consisting of graphs for which the...
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Nordhaus-Gaddum results for the weakly convex domination number of a graph
PublikacjaArtykuł dotyczy ograniczenia z góry i z dołu (ze względu na ilość wierzchołków) sumy i iloczynu liczb dominowania wypukłego grafu i jego dopełnienia.
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Graphs with equal domination and 2-distance domination numbers
PublikacjaW publikacji scharakteryzowane są wszystkie te drzewa i grafy jednocykliczne, w których liczba dominowania oraz liczba 2-dominowania na odległość są sobie równe.
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Preface
PublikacjaThis special issue of Discussiones Mathematice Graph Theory (DMGT) is dedicated to selected papers presented at the 13th Workshop on Graph Theory: Colourings, Independence and Domination (CID) held on 18-23 September 2009 in Szklarska Poręba, Poland. It continues a series of international workshops: 1993-1997 in Lubiatów, 1998-2001 in Gronów, and 2003-2007 in Karpacz. The meeting was organized by the Faculty of Mathematics, Computer...
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Optimal backbone coloring of split graphs with matching backbones
PublikacjaFor a graph G with a given subgraph H, the backbone coloring is defined as the mapping c: V(G) -> N+ such that |c(u)-c(v)| >= 2 for each edge uv \in E(H) and |c(u)-c(v)| >= 1 for each edge uv \in E(G). The backbone chromatic number BBC(G;H) is the smallest integer k such that there exists a backbone coloring with max c(V(G)) = k. In this paper, we present the algorithm for the backbone coloring of split graphs with matching backbone.
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Weakly connected domination subdivision numbers
PublikacjaLiczba podziału krawędzi dla dominowania słabo spójnego to najmniejsza liczba krawędzi jaką należy podzielić, aby wzrosła liczba dominowania słabo wypukłego. W pracy przedstawione są własności liczby podziału krawędzi dla dominowania słabo spójnego dla różnych grafów.
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Minimum vertex ranking spanning tree problem for chordal and proper interval graphs
PublikacjaW pracy rozważamy problem szukania, dla danego grafu prostego, drzewa spinającego, którego uporządkowana liczba chromatyczna jest minimalna. K.~Miyata i inni dowiedli w [Np-hardness proof and an approximation algorithm for the minimum vertex ranking spanning tree problem,Discrete Appl. Math. 154 (2006) 2402-2410], że odpowiedni problem decyzyjny jest NP-trudny już w przypadku pytania o istnienie uporządkowanego 4-pokolorowania....
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Relations between the domination parameters and the chromatic index of a graph
PublikacjaIn this paper we show bounds for the sum and the product of the domination parameters and the chromatic index of a graph. We alsopresent some families of graphs for which these bounds are achieved.
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Efficient list cost coloring of vertices and/or edges of bounded cyclicity graphs
PublikacjaW artykule rozważamy listowo-kosztowe kolorowanie wierzchołków i krawędzi grafu w modelu wierzchołkowym, krawędziowym, totalnym i pseudototalnym. Stosujemy programowanie dynamiczne w celu otrzymania algorytmów wielomianowych dla drzew. Następnie uogólniamy to podejście na dowolne grafy z ograniczonymi liczbami cyklomatycznymi i na ich multikolorowania.
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Preface of guest editors
PublikacjaA special issue of Discussiones Mathematice Graph Theory (DMGT) is dedicated to selected papers presented at the 12th Workshop on Graph Theory: Colourings, Independence and Domination (CID) held on 16-21 September 2007 in Karpacz, Poland. It continues a series of international workshops: 1993-1997 in Lubiatów, 1998-2001 in Gronów, 2003 and 2005 in Karpacz. About 70 participants formed the audience of six invited lectures and 68...
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Restrained differential of a graph
PublikacjaGiven a graph $G=(V(G), E(G))$ and a vertex $v\in V(G)$, the {open neighbourhood} of $v$ is defined to be $N(v)=\{u\in V(G) :\, uv\in E(G)\}$. The {external neighbourhood} of a set $S\subseteq V(G)$ is defined as $S_e=\left(\cup_{v\in S}N(v)\right)\setminus S$, while the \emph{restrained external neighbourhood} of $S$ is defined as $S_r=\{v\in S_e : N(v)\cap S_e\neq \varnothing\}$. The restrained differential of a graph $G$ is...
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T-colorings, divisibility and circular chromatic number
PublikacjaLet T be a T-set, i.e., a finite set of nonnegative integers satisfying 0 ∈ T, and G be a graph. In the paper we study relations between the T-edge spans espT (G) and espd⊙T (G), where d is a positive integer and d ⊙ T = {0 ≤ t ≤ d (max T + 1): d |t ⇒ t/d ∈ T} . We show that espd⊙T (G) = d espT (G) − r, where r, 0 ≤ r ≤ d − 1, is an integer that depends on T and G. Next we focus on the case T = {0} and show that espd⊙{0} (G) =...
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