# Alternation graphs

Halldorsson, Magnus and Kitaev, Sergey and Pyatkin, Artem
(2011)
*Alternation graphs.*
In:
Graph-theoretic concepts in computer science.
Lecture Notes in Computer Science
.
Springer-Verlag Berlin, Berlin, pp. 191-202.
ISBN 9783642258695

## Abstract

A graph G = (V,E) is an alternation graph if there exists a word W over the alphabet V such that letters x and y alternate in W if and only if (x,y) ∈ E for each x ≠ y. In this paper we give an effective characterization of alternation graphs in terms of orientations. Namely, we show that a graph is an alternation graph if and only if it admits a semi-transitive orientation defined in the paper. This allows us to prove a number of results about alternation graphs, in particular showing that the recognition problem is in NP, and that alternation graphs include all 3-colorable graphs. We also explore bounds on the size of the word representation of the graph. A graph G is a k-alternation graph if it is represented by a word in which each letter occurs exactly k times; the alternation number of G is the minimum k for which G is a k-alternation graph. We show that the alternation number is always at most n, while there exist graphs for which it is n/2.

Item type: | Book Section |
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ID code: | 34557 |

Keywords: | alternation graphs, computer science, recognition problem, Electronic computers. Computer science, Computational Theory and Mathematics |

Subjects: | Science > Mathematics > Electronic computers. Computer science |

Department: | Faculty of Science > Computer and Information Sciences |

Depositing user: | Pure Administrator |

Date deposited: | 09 Nov 2011 15:08 |

Last modified: | 05 Jan 2018 06:15 |

URI: | https://strathprints.strath.ac.uk/id/eprint/34557 |

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