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Showing 1 to 5 of 5 for “"Graph Homomorphism"”.
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Topos-like Properties in Two Categories of Graphs and Graph-like Features in an Abstract Category
In the study of the Category of Graphs, the usual notion of a graph is that of a simple graph with at most one loop on any vertex, and the usual notion of a graph homomorphism is a mapping of graphs that sends vertices to vertices, edges to edges, and preserves incidence of the mapped vertices and …
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Topos-like Properties in Two Categories of Graphs and Graph-like Features in an Abstract Category
In the study of the Category of Graphs, the usual notion of a graph is that of a simple graph with at most one loop on any vertex, and the usual notion of a graph homomorphism is a mapping of graphs that sends vertices to vertices, edges to edges, and preserves incidence of the mapped vertices and …
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On the Attainability of Upper Bounds for the Circular Chromatic Number of <em>K</em><sub>4</sub>-Minor-Free Graphs.
<p>Let <em>G</em> be a graph. For <em>k</em> ≥ <em>d</em> ≥ 1, a <em>k</em>/<em>d</em> -coloring of <em>G</em> is a coloring <em>c</em> of vertices of <em>G</em> with colors 0, 1, 2, . . ., <em>k</em> - 1, such that <em>d</em> ≤ | <em>c</em>(<em>x</em>) - <em>c</em>(<em>y</em>) | ≤ <em>k</em> - …
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D-colorable digraphs with large girth
<p>In 1959 Paul Erdos (<italic>Graph theory and probability</italic>, Canad. J. Math. <bold>11</bold> (1959), 34-38) famously proved, nonconstructively, that there exist graphs that have both arbitrarily large girth and arbitrarily large chromatic number. This result, along with its proof, has had …
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D-colorable digraphs with large girth
<p>In 1959 Paul Erdos (<italic>Graph theory and probability</italic>, Canad. J. Math. <bold>11</bold> (1959), 34-38) famously proved, nonconstructively, that there exist graphs that have both arbitrarily large girth and arbitrarily large chromatic number. This result, along with its proof, has had …