Tree loop graphs

  • Authors:

  • Liliana Alcón;Márcia R. Cerioli;Celina M. H. de Figueiredo;Marisa Gutierrez;João Meidanis

  • Affiliations:

  • Departamento de Matemática, Universidad Nacional de La Plata, CC 172, (1900) La Plata, Argentina;Instituto de Matemática and COPPE/Sistemas, Universidade Federal do Rio de Janeiro, Caixa Postal 68511, 21945-970, Rio de Janeiro, RJ, Brazil;Instituto de Matemática and COPPE/Sistemas, Universidade Federal do Rio de Janeiro, Caixa Postal 68511, 21945-970, Rio de Janeiro, RJ, Brazil;Departamento de Matemática, Universidad Nacional de La Plata, CC 172, (1900) La Plata, Argentina;Scylla Bioinformatics and Instituto de Computação, Universidade Estadual de Campinas, Caixa Postal 6176, 13084-971, Campinas, SP, Brazil

  • Venue:
  • Discrete Applied Mathematics
  • Year:
  • 2007

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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.