5 research outputs found

    The graph distance game and some graph operations

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    In the graph distance game, two players alternate in constructing a max- imal path. The objective function is the distance between the two endpoints of the path, which one player tries to maximize and the other tries to minimize. In this paper we examine the distance game for various graph operations: the join, the corona and the lexicographic product of graphs. We provide general bounds and exact results for special graphsPostprint (published version

    Jogos combinatórios em grafos: jogo Timber e jogo de Coloração

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    Studies three competitive combinatorial games. The timber game is played in digraphs, with each arc representing a domino, and the arc direction indicates the direction in which it can be toppled, causing a chain reaction. The player who topples the last domino is the winner. A P-position is an orientation of the edges of a graph in which the second player wins. If the graph has cycles, then the graph has no P-positions and, for this reason, timber game is only interesting when played in trees. We determine the number of P-positions in three caterpillar families and a lower bound for the number of P-positions in any caterpillar. Moreover, we prove that a tree has P-positions if, and only if, it has an even number of edges. In the coloring game, Alice and Bob take turns properly coloring the vertices of a graph, Alice trying to minimize the number of colors used, while Bob tries to maximize them. The game chromatic number is the smallest number of colors that ensures that the graph can be properly colored despite of Bob's intention. We determine the game chromatic number for three forest subclasses (composed by caterpillars), we present two su cient conditions and two necessary conditions for any caterpillar to have game chromatic number equal to 4. In the marking game, Alice and Bob take turns selecting the unselected vertices of a graph, and Alice tries to ensure that for some integer k, every unselected vertex has at most k − 1 neighbors selected. The game coloring number is the smallest k possible. We established lower and upper bounds for the Nordhaus-Gaddum type inequality for the number of P-positions of a caterpillar, the game chromatic and coloring numbers in any graph.Estudo de três jogos combinatórios competitivos. O jogo timber é jogado em digrafos, sendo que cada arco representa um dominó, e o sentido do arco indica o sentido em que o mesmo pode ser derrubado, causando um efeito em cadeia. O jogador que derrubar o último dominó é o vencedor. Uma P-position é uma orientação das arestas de um grafo na qual o segundo jogador ganha. Se o grafo possui ciclos, então não há P-positions e, por este motivo, o jogo timber só é interessante quando jogado em árvores. Determinamos o número de P-positions em três famílias de caterpillars e um limite inferior para o número de P-positions em uma caterpillar qualquer. Além disto, provamos que uma árvore qualquer possui P-positions se, e somente se, possui quantidade par de arestas. No jogo de coloração, Alice e Bob se revezam colorindo propriamente os vértices de um grafo, sendo que Alice tenta minimizar o número de cores, enquanto Bob tenta maximizá-lo. O número cromático do jogo é o menor número de cores que garante que o grafo pode ser propriamente colorido apesar da intenção de Bob. Determinamos o número cromático do jogo para três subclasses de orestas (compostas por caterpillars), apresentamos duas condições su cientes e duas condições necessárias para qualquer caterpillar ter número cromático do jogo igual a 4. No jogo de marcação, Alice e Bob selecionam alternadamente os vértices não selecionados de um grafo, e Alice tenta garantir que para algum inteiro k, todo vértice não selecionado tem no máximo k − 1 vizinhos selecionados. O número de coloração do jogo é o menor k possível. Estabelecemos limites inferiores e superiores para a relação do tipo Nordhaus-Gaddum referente ao número de P-positions de uma caterpillar, aos números cromático e de coloração do jogo em um grafo qualquer

    The Moving Page

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    This paper investigates transitional states of spaces between images, moving images, and the use of sketchbook/page works through a questioning and auto-ethnographic approach to research and practice. Viewing illustration as a refexive space, the investigations demonstrate exchangesbetween authorship, interaction, narrative, time, and space. Valuing the ‘in-between’ states that exist between the unfnished and fnished, the research questions notions of in-fux, moving, nebulous states. Through alternative publishing forms, the research concerns dissemination through emerging digital platforms

    The Moving Page

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    This paper investigates transitional states of spaces between images, moving images, and the use of sketchbook/page works through a questioning and auto-ethnographic approach to research and practice. Viewing illustration as a refexive space, the investigations demonstrate exchangesbetween authorship, interaction, narrative, time, and space. Valuing the ‘in-between’ states that exist between the unfnished and fnished, the research questions notions of in-fux, moving, nebulous states. Through alternative publishing forms, the research concerns dissemination through emerging digital platforms

    SiJIS 6-2016 Full Issue

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