Factorizations of Complete Graphs into Spanning Trees with All Possible Maximum Degrees

2009 ◽  
pp. 334-344 ◽  
Author(s):  
Petr Kovář ◽  
Michael Kubesa
Keyword(s):  
Spanning Trees ◽  
Complete Graphs

scholarly journals Edge-disjoint rainbow spanning trees in complete graphs

2016 ◽  
Vol 57 ◽  
pp. 71-84 ◽  
Author(s):  
James M. Carraher ◽  
Stephen G. Hartke ◽  
Paul Horn
Keyword(s):  
Spanning Trees ◽  
Complete Graphs ◽  
Edge Disjoint

scholarly journals Spanning Trees of Complete Graphs and Cycles

2021 ◽  
Author(s):  
◽  
Minjin Enkhjargal
Keyword(s):  
Spanning Trees ◽  
Complete Graphs

Cyclic decompositions of complete graphs into spanning trees

2004 ◽  
Vol 24 (2) ◽  
pp. 345 ◽  
Author(s):  
Dalibor Fronček
Keyword(s):  
Spanning Trees ◽  
Complete Graphs

Maximizing spanning trees in almost complete graphs

Networks ◽  
1997 ◽  
Vol 30 (1) ◽  
pp. 23-30 ◽  
Author(s):  
Bryan Gilbert ◽  
Wendy Myrvold
Keyword(s):  
Spanning Trees ◽  
Complete Graphs

scholarly journals On the Spanning Trees of the Hypercube and other Products of Graphs

10.37236/2510 ◽  
2012 ◽  
Vol 19 (4) ◽  
Author(s):  
Olivier Bernardi
Keyword(s):  
Spanning Tree ◽  
Spanning Trees ◽  
Cartesian Product ◽  
Product Formula ◽  
General Context ◽  
Complete Graphs ◽  
Independence Property ◽  
Number Of Spanning Trees ◽  
Tree Approach

We give two combinatorial proofs of a product formula for the number of spanning trees of the $n$-dimensional hypercube. The first proof is based on the assertion that if one chooses a uniformly random rooted spanning tree of the hypercube and orient each edge from parent to child, then the parallel edges of the hypercube get orientations which are independent of one another. This independence property actually holds in a more general context and has intriguing consequences. The second proof uses some "killing involutions'' in order to identify the factors in the product formula. It leads to an enumerative formula for the spanning trees of the $n$-dimensional hypercube augmented with diagonals edges, counted according to the number of edges of each type. We also discuss more general formulas, obtained using a matrix-tree approach, for the number of spanning trees of the Cartesian product of complete graphs.

scholarly journals Rainbow spanning trees in properly coloured complete graphs

2018 ◽  
Vol 247 ◽  
pp. 97-101 ◽  
Author(s):  
József Balogh ◽  
Hong Liu ◽  
Richard Montgomery
Keyword(s):  
Spanning Trees ◽  
Complete Graphs

scholarly journals Multicolored isomorphic spanning trees in complete graphs

2002 ◽  
Vol Vol. 5 ◽  
Author(s):  
Gregory Constantine
Keyword(s):  
Complete Graph ◽  
Spanning Trees ◽  
Complete Graphs ◽  
Edge Disjoint ◽  
International Audience

International audience Can a complete graph on an even number n (>4) of vertices be properly edge-colored with n-1 colors in such a way that the edges can be partitioned into edge disjoint colorful isomorphic spanning trees? A spanning treee is colorful if all n-1 colors occur among its edges. It is proved that this is possible to accomplish whenever n is a power of two, or five times a power of two.

scholarly journals Bi-cyclic decompositions of complete graphs into spanning trees

2007 ◽  
Vol 307 (11-12) ◽  
pp. 1317-1322 ◽  
Author(s):  
Dalibor Froncek
Keyword(s):  
Spanning Trees ◽  
Complete Graphs
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