Independent trees in graphs |
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Authors: | Andreas Huck |
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Institution: | (1) Institut für Mathematik, Universität Hannover, Welfengarten 1, 30167 Hannover, Germany |
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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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Keywords: | |
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