Descendants and ascendants in binary trees.

Panholzer, Alois; Prodinger, Helmut

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Completely Independent Spanning Trees in (Partial) k-Trees

Masayoshi Matsushita, Yota Otachi, Toru Araki (2015)

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Two spanning trees T1 and T2 of a graph G are completely independent if, for any two vertices u and v, the paths from u to v in T1 and T2 are internally disjoint. For a graph G, we denote the maximum number of pairwise completely independent spanning trees by cist(G). In this paper, we consider cist(G) when G is a partial k-tree. First we show that [k/2] ≤ cist(G) ≤ k − 1 for any k-tree G. Then we show that for any p ∈ {[k/2], . . . , k − 1}, there exist infinitely many k-trees G such...