Bar k-Visibility Graphs
| Autor: | MohammadAli Safari, William T. Trotter, Joshua D. Laison, Alice M. Dean, Ellen Gethner, William S. Evans |
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| Rok vydání: | 2007 |
| Předmět: |
Discrete mathematics
Book embedding General Computer Science High Energy Physics::Phenomenology Trapezoid graph 1-planar graph Computer Science Applications Theoretical Computer Science Planar graph Combinatorics Indifference graph symbols.namesake Pathwidth Computational Theory and Mathematics Chordal graph symbols High Energy Physics::Experiment Bound graph Geometry and Topology Mathematics |
| Zdroj: | Journal of Graph Algorithms and Applications. 11:45-59 |
| ISSN: | 1526-1719 |
| DOI: | 10.7155/jgaa.00136 |
| Popis: | Let S be a set of horizontal line segments, or bars, in the plane. We say that G is a bar visibility graph, and S its bar visibility representation, if there exists a one-to-one correspondence between vertices of G and bars in S, such that there is an edge between two vertices in G if and only if there exists an unobstructed vertical line of sight between their corresponding bars. If bars are allowed to see through each other, the graphs representable in this way are precisely the interval graphs. We consider representations in which bars are allowed to see through at most k other bars. Since all bar visibility graphs are planar, we seek measurements of closeness to planarity for bar k-visibility graphs. We obtain an upper bound on the number of edges in a bar k-visibility graph. As a consequence, we obtain an upper bound of 12 on the chromatic number of bar 1-visibility graphs, and a tight upper bound of 8 on the size of the largest complete bar 1-visibility graph. We also consider the thickness of bar k-visibility graphs, obtaining an upper bound of 4 when k = 1, and a bound that is quadratic in k for k > 1. |
| Databáze: | OpenAIRE |
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