Completely Independent Spanning Trees in Maximal Planar Graphs

Authors:
Toru Hasunuma
Affiliations:
-
Venue:
WG '02 Revised Papers from the 28th International Workshop on Graph-Theoretic Concepts in Computer Science
Year:
2002

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Abstract

Let G be a graph. Let T1, T2, . . . , Tk be spanning trees in G. If for any two vertices u, v in G, the paths from u to v in T1, T2, . . . , Tk are pairwise openly disjoint, then we say that T1, T2, . . . , Tk are completely independent spanning trees in G. In this paper, we show that there are two completely independent spanning trees in any 4-connected maximal planar graph. Our proof induces a linear-time algorithm for finding such trees. Besides, we show that given a graph G, the problem of deciding whether there exist two completely independent spanning trees in G is NP-complete.