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Search results for: combinatorics
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Interpolation properties of domination parameters of a graph
PublicationAn integer-valued graph function π is an interpolating function if a set π(T(G))={π(T): T∈TT(G)} consists of consecutive integers, where TT(G) is the set of all spanning trees of a connected graph G. We consider the interpolation properties of domination related parameters.
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Influence of edge subdivision on the convex domination number
PublicationWe study the influence of edge subdivision on the convex domination number. We show that in general an edge subdivision can arbitrarily increase and arbitrarily decrease the convex domination number. We also find some bounds for unicyclic graphs and we investigate graphs G for which the convex domination number changes after subdivision of any edge in G.
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On-line Ramsey Numbers of Paths and Cycles
PublicationConsider a game played on the edge set of the infinite clique by two players, Builder and Painter. In each round, Builder chooses an edge and Painter colours it red or blue. Builder wins by creating either a red copy of $G$ or a blue copy of $H$ for some fixed graphs $G$ and $H$. The minimum number of rounds within which Builder can win, assuming both players play perfectly, is the \emph{on-line Ramsey number} $\tilde{r}(G,H)$. In...
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Certified domination
PublicationImagine that we are given a set D of officials and a set W of civils. For each civil x ∈ W, there must be an official v ∈ D that can serve x, and whenever any such v is serving x, there must also be another civil w ∈ W that observes v, that is, w may act as a kind of witness, to avoid any abuse from v. What is the minimum number of officials to guarantee such a service, assuming a given social network? In this paper, we introduce...
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Marek Kubale prof. dr hab. inż.
PeopleDetails concerning: Qualifications, Experiences, Editorial boards, Ph.D. theses supervised, Books, and Recent articles can be found at http://eti.pg.edu.pl/katedra-algorytmow-i-modelowania-systemow/Marek_KubaleGoogle ScholarSylwetka prof. Marka Kubalego Prof. Marek Kubale pracuje na Wydziale ETI Politechniki Gdańskiej nieprzerwanie od roku 1969. W tym czasie napisał ponad 150 prac naukowych, w tym ponad 40 z listy JCR. Ponadto...
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On trees attaining an upper bound on the total domination number
PublicationA total dominating set of a graph G is a set D of vertices of G such that every vertex of G has a neighbor in D. The total domination number of a graph G, denoted by γ_t(G), is the minimum cardinality of a total dominating set of G. Chellali and Haynes [Total and paired-domination numbers of a tree, AKCE International Journal of Graphs and Combinatorics 1 (2004), 69-75] established the following upper bound on the total domination...
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Average Size of a Suffix Tree for Markov Sources
PublicationWe study a suffix tree built from a sequence generated by a Markovian source. Such sources are more realistic probabilistic models for text generation, data compression, molecular applications, and so forth. We prove that the average size of such a suffix tree is asymptotically equivalent to the average size of a trie built over n independentsequences from the same Markovian source. This equivalenceis only known for memoryless...
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Workshop on Graph Theory
EventsThe Gdańsk Workshop on Graph Theory (GWGT) is an annual, informal workshop whose goal is to provide a forum for scientists to meet, present their work, interact, and establish collaborations in the field of Graph Theory
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Types of Markov Fields and Tilings
PublicationThe method of types is one of the most popular techniques in information theory and combinatorics. However, thus far the method has been mostly applied to one-dimensional Markov processes, and it has not been thoroughly studied for general Markov fields. Markov fields over a finite alphabet of size m ≥ 2 can be viewed as models for multi-dimensional systems with local interactions. The locality of these interactions is represented...
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Maciej Dziemiańczuk dr
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