The plane-width of graphs
Copyright policy )The plane-width of graphs
Map vertices of a graph to (not necessarily distinct) points of the plane so that two adjacent vertices are mapped at least a unit distance apart. The plane-width of a graph is the minimum diameter of the image of the vertex set over all such mappings. We establish a relation between the plane-width of a graph and its chromatic number, and connect it to other well-known areas, including the circular chromatic number and the problem of packing unit discs in the plane. We also investigate how plane-width behaves under various operations, such as homomorphism, disjoint union, complement, and the Cartesian product.
circular chromatic number, FOS: Computer and information sciences, plane-width, Distance in graphs, Discrete Mathematics (cs.DM), Graph representations (geometric and intersection representations, etc.), info:eu-repo/classification/udc/519.17, Planar graphs; geometric and topological aspects of graph theory, Euclidean analytic geometry, Coloring of graphs and hypergraphs, chromatic number, packing non-overlapping unit discs, Informatique mathématique, packing non-overlapping unit disks, realization of a graph, Computer Science - Discrete Mathematics
circular chromatic number, FOS: Computer and information sciences, plane-width, Distance in graphs, Discrete Mathematics (cs.DM), Graph representations (geometric and intersection representations, etc.), info:eu-repo/classification/udc/519.17, Planar graphs; geometric and topological aspects of graph theory, Euclidean analytic geometry, Coloring of graphs and hypergraphs, chromatic number, packing non-overlapping unit discs, Informatique mathématique, packing non-overlapping unit disks, realization of a graph, Computer Science - Discrete Mathematics
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