The convexity of induced paths of order three
نویسندگان
چکیده
In this paper, we introduce a new convexity on graphs similar to the well known P3convexity [3], which we will call P ∗ 3 -convexity. We show that several P ∗ 3 -convexity parameters (hull number, convexity number, Carathéodory number, Radon number, interval number and percolation time) are NP-hard even on bipartite graphs. We show a strong relation between this convexity and the well known geodesic convexity [11], which implies several NP-hardness results on the geodesic convexity. We also obtain linear time algorithms to determine all those parameters on the above mentioned convexities for some graph classes.
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ورودعنوان ژورنال:
- Electronic Notes in Discrete Mathematics
دوره 44 شماره
صفحات -
تاریخ انتشار 2013