Given a graph G and a pair of vertices the interval is the set of all vertices that are in some shortest path between u and v. Given a subset X of vertices of G, the interval of X, is the union of the intervals for all pairs of vertices in X and we say that X is geodetic if its interval do coincide with the set of vertices in the graph. A minimum geodetic set is a minimum cardinality geodetic set of G. The problem of computing a minimum geodetic set is known to be NP-Hard for general graphs but is known to be polynomially solvable for maximal outerplanar graphs. In this paper we show a polynomial time algorithm for finding a minimum geodetic set in general outerplanar graphs.

Mezzini, M. (2018). Polynomial time algorithm for computing a minimum geodetic set in outerplanar graphs. THEORETICAL COMPUTER SCIENCE [10.1016/j.tcs.2018.05.032].

### Polynomial time algorithm for computing a minimum geodetic set in outerplanar graphs

#### Abstract

Given a graph G and a pair of vertices the interval is the set of all vertices that are in some shortest path between u and v. Given a subset X of vertices of G, the interval of X, is the union of the intervals for all pairs of vertices in X and we say that X is geodetic if its interval do coincide with the set of vertices in the graph. A minimum geodetic set is a minimum cardinality geodetic set of G. The problem of computing a minimum geodetic set is known to be NP-Hard for general graphs but is known to be polynomially solvable for maximal outerplanar graphs. In this paper we show a polynomial time algorithm for finding a minimum geodetic set in general outerplanar graphs.
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2018
Mezzini, M. (2018). Polynomial time algorithm for computing a minimum geodetic set in outerplanar graphs. THEORETICAL COMPUTER SCIENCE [10.1016/j.tcs.2018.05.032].
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Utilizza questo identificativo per citare o creare un link a questo documento: `https://hdl.handle.net/11590/338384`
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