par Biniaz, Ahmad;Bose, Prosenjit 
;Ooms, Aurélien ;Verdonschot, Sander
Référence Leibniz international proceedings in informatics, 101, page (141-1412)
Publication Publié, 2018-06
;Ooms, Aurélien ;Verdonschot, SanderRéférence Leibniz international proceedings in informatics, 101, page (141-1412)
Publication Publié, 2018-06
Article révisé par les pairs
| Résumé : | An edge guard set of a plane graph G is a subset of edges of G such that each face of G is incident to an endpoint of an edge in . Such a set is said to guard G. We improve the known upper bounds on the number of edges required to guard any n-vertex embedded planar graph G: 1. We present a simple inductive proof for a theorem of Everett and Rivera-Campo (1997) that G can be guarded with at most 2 5 n edges, then extend this approach with a deeper analysis to yield an improved bound of 3 8 n edges for any plane graph. 2. We prove that there exists an edge guard set of G with at most n 3 +α 9 edges, where α is the number of quadrilateral faces in G. This improves the previous bound of n 3 + α by Bose, Kirkpatrick, and Li (2003). Moreover, if there is no short path between any two quadrilateral faces in G, we show that n 3 edges su ce, removing the dependence on α. |
