Publikacje
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wszystkich: 46
Katalog Publikacji
Rok 2023
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Edge coloring of graphs of signed class 1 and 2
PublikacjaRecently, Behr (2020) introduced a notion of the chromatic index of signed graphs and proved that for every signed graph (G, σ) it holds that ∆(G) ≤ χ′(G,σ) ≤ ∆(G) + 1, where ∆(G) is the maximum degree of G and χ′ denotes its chromatic index. In general, the chromatic index of (G, σ) depends on both the underlying graph G and the signature σ. In the paper we study graphs G for which χ′(G, σ) does not depend on σ. To this aim we...
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Potyczki algorytmiczne, czyli Alicja i Bogdan w nowych sytuacjach. 3. Alicja i Bogdan remontują mieszkanie.
PublikacjaPoniższe zagadki nawiązują z jednej strony do problemu kafelkowania płaszczyzny, który jest nierozstrzygalny, z drugiej do problemu rozkroju wstęgi, który jest NP-trudny. Jednakże przypadki szczególne, które tu rozważamy, nie są tak trudne i mogą być rozwiązane za pomocą algorytmów działających w czasie wielomianowym.
Rok 2022
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Infinite chromatic games
PublikacjaIn the paper we introduce a new variant of the graph coloring game and a new graph parameter being the result of the new game. We study their properties and get some lower and upper bounds, exact values for complete multipartite graphs and optimal, often polynomial-time strategies for both players provided that the game is played on a graph with an odd number of vertices. At the end we show that both games, the new and the classic...
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Weighted 2-sections and hypergraph reconstruction
PublikacjaIn the paper we introduce the notion of weighted 2-sections of hypergraphs with integer weights and study the following hypergraph reconstruction problems: (1) Given a weighted graph , is there a hypergraph H such that is its weighted 2-section? (2) Given a weighted 2-section , find a hypergraph H such that is its weighted 2-section. We show that (1) is NP-hard even if G is a complete graph or integer weights w does not exceed...
Rok 2021
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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) =...
Rok 2019
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2-Coloring number revisited
Publikacja2-Coloring number is a parameter, which is often used in the literature to bound the game chromatic number and other related parameters. However, this parameter has not been precisely studied before. In this paper we aim to fill this gap. In particular we show that the approximation of the game chromatic number by the 2-coloring number can be very poor for many graphs. Additionally we prove that the 2-coloring number may grow...
Rok 2018
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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.
Rok 2016
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An O ( n log n ) algorithm for finding edge span of cacti
PublikacjaLet G=(V,E) be a nonempty graph and xi be a function. In the paper we study the computational complexity of the problem of finding vertex colorings c of G such that: (1) |c(u)-c(v)|>=xi(uv) for each edge uv of E; (2) the edge span of c, i.e. max{|c(u)-c(v)|: uv belongs to E}, is minimal. We show that the problem is NP-hard for subcubic outerplanar graphs of a very simple structure (similar to cycles) and polynomially solvable for...
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Multi-level Virtualization and Its Impact on System Performance in Cloud Computing
PublikacjaThe results of benchmarking tests of multi-level virtualized environments are presented. There is analysed the performance impact of hardware virtualization, container-type isolation and programming level abstraction. The comparison is made on the basis of a proposed score metric that allows you to compare different aspects of performance. There is general performance (CPU and memory), networking, disk operations and application-like...
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On the hardness of computing span of subcubic graphs
PublikacjaIn the paper we study the problem of finding ξ-colorings with minimal span, i.e. the difference between the largest and the smallest color used.
Rok 2015
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Interval incidence graph coloring
PublikacjaIn this paper we introduce a concept of interval incidence coloring of graphs and survey its general properties including lower and upper bounds on the number of colors. Our main focus is to determine the exact value of the interval incidence coloring number χii for selected classes of graphs, i.e. paths, cycles, stars, wheels, fans, necklaces, complete graphs and complete k-partite graphs. We also study the complexity of the...
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The Backbone Coloring Problem for Bipartite Backbones
PublikacjaLet G be a simple graph, H be its spanning subgraph and λ≥2 be an integer. By a λ -backbone coloring of G with backbone H we mean any function c that assigns positive integers to vertices of G in such a way that |c(u)−c(v)|≥1 for each edge uv∈E(G) and |c(u)−c(v)|≥λ for each edge uv∈E(H) . The λ -backbone chromatic number BBCλ(G,H) is the smallest integer k such that there exists a λ -backbone coloring c of G with backbone H satisfying...
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The computational complexity of the backbone coloring problem for bounded-degree graphs with connected backbones
PublikacjaGiven a graph G, a spanning subgraph H of G and an integer λ>=2, a λ-backbone coloring of G with backbone H is a vertex coloring of G using colors 1, 2, ..., in which the color difference between vertices adjacent in H is greater than or equal to lambda. The backbone coloring problem is to find such a coloring with maximum color that does not exceed a given limit k. In this paper, we study the backbone coloring problem for bounded-degree...
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The computational complexity of the backbone coloring problem for planar graphs with connected backbones
PublikacjaIn the paper we study the computational complexity of the backbone coloring problem for planar graphs with connected backbones. For every possible value of integer parameters λ≥2 and k≥1 we show that the following problem: Instance: A simple planar graph GG, its connected spanning subgraph (backbone) HH. Question: Is there a λ-backbone coloring c of G with backbone H such that maxc(V(G))≤k? is either NP-complete or polynomially...
Rok 2014
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Interval incidence coloring of bipartite graphs
PublikacjaIn this paper we study the problem of interval incidence coloring of bipartite graphs. We show the upper bound for interval incidence coloring number (χii) for bipartite graphs χii≤2Δ, and we prove that χii=2Δ holds for regular bipartite graphs. We solve this problem for subcubic bipartite graphs, i.e. we fully characterize the subcubic graphs that admit 4, 5 or 6 coloring, and we construct a linear time exact algorithm for subcubic...
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The Backbone Coloring Problem for Small Graphs
PublikacjaIn this paper we investigate the values of the backbone chromatic number, derived from a mathematical model for the problem of minimization of bandwidth in radio networks, for small connected graphs and connected backbones (up to 7 vertices). We study the relationship of this parameter with the structure of the graph and compare the results with the solutions obtained using the classical graph coloring algorithms (LF, IS), modified...
Rok 2012
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A Developer's View of Application Servers Interoperability
PublikacjaThe paper describes analysis of application servers interoperability that considers both the available level of integration and the required level of development complexity. Development complexity ranges from simple GUI operations to changes of undocumented features in configuration files. We verify if an integration can be established on a given level of development complexity, rather than verify if it is objectively feasible....
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Minimalizacja szerokości pasma w sieciach radiowych metodami szkieletowego kolorowania grafów
PublikacjaArtykuł poświęcony jest szkieletowemu kolorowaniu grafów, które jest matematycznym modelem dla problemu minimalizacji szerokości pasma w sieciach radiowych. Badamy w nim zależność szkieletowej liczby chromatycznej od parametrów zagadnienia. Dowodzimy, że dla dużych wartości parametrów ta zależność jest liniowa.
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Uczelniane eBiuro jako usługa
PublikacjaArtykuł jest wprowadzeniem w tematykę rozwijanych na Politechnice Gdańskiej usług projektu eBiuro, mającego usprawnić działanie administracji Uczelni. Szczególny nacisk położono na kwestieinterakcji z innymi działającymi już w środowisku systemami oraz na zaplanowanie integracji z usługami nowo powstającymi w ramach równoległego projektu eUczelnia. Artykuł powstał m.in. na podstawieopracowania przygotowanego przez autora dla Centrum...
Rok 2011
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Consensus models: Computational complexity aspects in modern approaches to the list coloring problem
PublikacjaArtykuł poświęcony jest nowym modelom konsensusowego kolorowania grafów. Artykuł zawiera omówienie trzech takich modeli, analizę ich złożoności obliczeniowej oraz wielomianowy algorytm dla częściowych k-drzew, dla tzw. modelu addytywnego.