Abstract
IfG is a finite undirected graph ands is a vertex ofG, then two spanning treesT 1 andT 2 inG are calleds — independent if for each vertexx inG the paths fromx tos inT 1 andT 2 are openly disjoint. It is known that the following statement is true fork≤3: IfG isk-connected, then there arek pairwises — independent spanning, trees inG. As a main result we show that this statement is also true fork=4 if we restrict ourselves to planar graphs. Moreover we consider similar statements for weaklys — independent spanning trees (i.e., the tree paths from a vertex tos are edge disjoint) and for directed graphs.
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Huck, A. Independent trees in graphs. Graphs and Combinatorics 10, 29–45 (1994). https://doi.org/10.1007/BF01202468
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DOI: https://doi.org/10.1007/BF01202468