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Wyniki wyszukiwania dla: teoria grafow
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Building a Nest by an Automaton
PublikacjaA robot modeled as a deterministic finite automaton has to build a structure from material available to it. The robot navigates in the infinite oriented grid $Z x Z$. Some cells of the grid are full (contain a brick) and others are empty. The subgraph of the grid induced by full cells, called the {\em field}, is initially connected. The (Manhattan) distance between the farthest cells of the field is called its {\em span}. The robot...
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On-line Search in Two-Dimensional Environment
PublikacjaWe consider the following on-line pursuit-evasion problem. A team of mobile agents called searchers starts at an arbitrary node of an unknown network. Their goal is to execute a search strategy that guarantees capturing a fast and invisible intruder regardless of its movements using as few searchers as possible. We require that the strategy is connected and monotone, that is, at each point of the execution the part of the graph...
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Finding small-width connected path decompositions in polynomial time
PublikacjaA connected path decomposition of a simple graph $G$ is a path decomposition $(X_1,\ldots,X_l)$ such that the subgraph of $G$ induced by $X_1\cup\cdots\cup X_i$ is connected for each $i\in\{1,\ldots,l\}$. The connected pathwidth of $G$ is then the minimum width over all connected path decompositions of $G$. We prove that for each fixed $k$, the connected pathwidth of any input graph can be computed in polynomial-time. This answers...
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Cops, a fast robber and defensive domination on interval graphs
PublikacjaThe game of Cops and ∞-fast Robber is played by two players, one controlling c cops, the other one robber. The players alternate in turns: all the cops move at once to distance at most one each, the robber moves along any cop-free path. Cops win by sharing a vertex with the robber, the robber by avoiding capture indefinitely. The game was proposed with bounded robber speed by Fomin et al. in “Pursuing a fast robber on a graph”,...
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Edge and Pair Queries-Random Graphs and Complexity
PublikacjaWe investigate two types of query games played on a graph, pair queries and edge queries. We concentrate on investigating the two associated graph parameters for binomial random graphs, and showing that determining any of the two parameters is NP-hard for bounded degree graphs.
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On the doubly connected domination number of a graph
PublikacjaW pracy została zdefiniowana liczba dominowania podwójnie spójnego i przedstawiono jej podstawowe własności.
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Graphs with convex domination number close to their order
PublikacjaW pracy opisane są grafy z liczbą dominowania wypukłego bliską ilości ich wierzchołków.
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Dominowanie w grafach
PublikacjaW pracy rozważanych jest pięć liczb dominowania: klasyczna liczba dominowania, liczba dominowania spójnego, liczba dominowania słabo spójnego, liczba dominowania słabo wypukłego i liczba dominowania wypukłego. Rozważane są pewne ograniczenia na liczby dominowania, równości między poszczególnymi liczbami, wpływ usuwania krawędzi lub zbioru krawędzi na liczby dominowania i NP-zupełność problemów dominowania.
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Lower bound on the distance k-domination number of a tree
PublikacjaW artykule przedstawiono dolne ograniczenie na liczbę k-dominowania w drzewach oraz scharakteryzowano wszystkie grafy ekstremalne.
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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.