Abstract
If a graph G contains two spanning trees T1,T2 such that for each two distinct vertices x,y of G, the (x,y)-path in each Ti has no common edge and no common vertex except for the two ends, then T1,T2 are called two completely independent spanning trees (CISTs) of G,i∈{1,2}. There are several results on the existence of two CISTs. In this paper, we prove that every 2-connected {claw, Z2}-free graph with minimum degree at least 4 contains two CISTs. The bound of the minimum degree in our result is best possible.
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