Tree loop graphs |
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| Institution: | 1. Departamento de Matemática, Universidad Nacional de La Plata, CC 172, (1900) La Plata, Argentina;2. Instituto de Matemática and COPPE/Sistemas, Universidade Federal do Rio de Janeiro, Caixa Postal 68511, 21945-970, Rio de Janeiro, RJ, Brazil;3. Scylla Bioinformatics and Instituto de Computação, Universidade Estadual de Campinas, Caixa Postal 6176, 13084-971, Campinas, SP, Brazil;1. Department of Computer Science and Center for Computational Molecular Biology, Brown University, 115 Waterman St, Box 1910, Providence, RI 02912, USA;2. Department of Computer Science and Engineering, University of California San Diego, APM 3132, 9500 Gilman Drive Dept. 0114, La Jolla, CA 92093-0114, USA;3. School of Computer Science, Tel Aviv University, Tel Aviv 69978, Israel |
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| Abstract: | Many problems involving DNA can be modeled by families of intervals. However, traditional interval graphs do not take into account the repeat structure of a DNA molecule. In the simplest case, one repeat with two copies, the underlying line can be seen as folded into a loop. We propose a new definition that respects repeats and define loop graphs as the intersection graphs of arcs of a loop. The class of loop graphs contains the class of interval graphs and the class of circular-arc graphs. Every loop graph has interval number 2. We characterize the trees that are loop graphs. The characterization yields a polynomial-time algorithm which given a tree decides whether it is a loop graph and, in the affirmative case, produces a loop representation for the tree. |
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