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MPI-I-98-1-006

A new characterization for parity graphs and a coloring problem with costs

Jansen, Klaus

January 1998, 16 pages.

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Status: available - back from printing

In this paper, we give a characterization for parity graphs. A graph is a parity graph, if and only if for every pair of vertices all minimal chains joining them have the same parity. We prove that $G$ is a parity graph, if and only if the cartesian product $G \times K_2$ is a perfect graph. Furthermore, as a consequence we get a result for the polyhedron corresponding to an integer linear program formulation of a coloring problem with costs. For the case that the costs $k_{v,3} = k_{v,c}$ for each color $c \ge 3$ and vertex $v \in V$, we show that the polyhedron contains only integral $0 / 1$ extrema if and only if the graph $G$ is a parity graph.

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URL to this document: https://domino.mpi-inf.mpg.de/internet/reports.nsf/NumberView/1998-1-006

Hide details for BibTeXBibTeX
@TECHREPORT{Jansen98-1-006,
  AUTHOR = {Jansen, Klaus},
  TITLE = {A new characterization for parity graphs and a coloring problem with costs},
  TYPE = {Research Report},
  INSTITUTION = {Max-Planck-Institut f{\"u}r Informatik},
  ADDRESS = {Im Stadtwald, D-66123 Saarbr{\"u}cken, Germany},
  NUMBER = {MPI-I-98-1-006},
  MONTH = {January},
  YEAR = {1998},
  ISSN = {0946-011X},
}