Anti-Ramsey Problems in Complete Bipartite Graphs for t Edge-Disjoint Rainbow Spanning Trees

2020 ◽  
Author(s):  
Yuxing Jia ◽  
Mei Lu ◽  
Yi Zhang
Keyword(s):  
Spanning Trees ◽  
Bipartite Graphs ◽  
Edge Disjoint ◽  
Complete Bipartite Graphs

scholarly journals A decomposition of complete bipartite graphs into edge-disjoint subgraphs with star components

1986 ◽  
Vol 58 (1) ◽  
pp. 93-95 ◽  
Author(s):  
Yoshimi Egawa ◽  
Masatsugu Urabe ◽  
Toshihito Fukuda ◽  
Seiichiro Nagoya
Keyword(s):  
Bipartite Graphs ◽  
Edge Disjoint ◽  
Complete Bipartite Graphs

scholarly journals Number of Spanning Trees of Different Products of Complete and Complete Bipartite Graphs

2014 ◽  
Vol 2014 ◽  
pp. 1-23 ◽  
Author(s):  
S. N. Daoud
Keyword(s):  
Tensor Product ◽  
Linear Algebra ◽  
Spanning Trees ◽  
Matrix Theory ◽  
Cartesian Product ◽  
Bipartite Graphs ◽  
Normal Product ◽  
Complete Bipartite Graphs ◽  
Composition Product ◽  
Number Of Spanning Trees

Spanning trees have been found to be structures of paramount importance in both theoretical and practical problems. In this paper we derive new formulas for the complexity, number of spanning trees, of some products of complete and complete bipartite graphs such as Cartesian product, normal product, composition product, tensor product, symmetric product, and strong sum, using linear algebra and matrix theory techniques.

scholarly journals Edge-disjoint spanners of complete bipartite graphs

2001 ◽  
Vol 234 (1-3) ◽  
pp. 65-76 ◽  
Author(s):  
Christian Laforest ◽  
Arthur L. Liestman ◽  
Thomas C. Shermer ◽  
Dominique Sotteau
Keyword(s):  
Bipartite Graphs ◽  
Edge Disjoint ◽  
Complete Bipartite Graphs

scholarly journals Complexity of Products of Some Complete and Complete Bipartite Graphs

2013 ◽  
Vol 2013 ◽  
pp. 1-25 ◽  
Author(s):  
S. N. Daoud
Keyword(s):  
Tensor Product ◽  
Spanning Trees ◽  
Cartesian Product ◽  
Bipartite Graphs ◽  
Matrix Analysis ◽  
Normal Product ◽  
Analysis Techniques ◽  
Complete Bipartite Graphs ◽  
Composition Product ◽  
Number Of Spanning Trees

The number of spanning trees in graphs (networks) is an important invariant; it is also an important measure of reliability of a network. In this paper, we derive simple formulas of the complexity, number of spanning trees, of products of some complete and complete bipartite graphs such as cartesian product, normal product, composition product, tensor product, and symmetric product, using linear algebra and matrix analysis techniques.

scholarly journals Computing the number of h-edge spanning forests in complete bipartite graphs

2014 ◽  
Vol Vol. 16 no. 1 (Analysis of Algorithms) ◽  
Author(s):  
Rebecca Stones
Keyword(s):  
Bipartite Graph ◽  
Spanning Trees ◽  
Analysis Of Algorithms ◽  
Complete Bipartite Graph ◽  
Bipartite Graphs ◽  
Spanning Forests ◽  
International Audience ◽  
Complete Bipartite Graphs ◽  
Number Of Spanning Trees

Analysis of Algorithms International audience Let fm,n,h be the number of spanning forests with h edges in the complete bipartite graph Km,n. Kirchhoff\textquoterights Matrix Tree Theorem implies fm,n,m+n-1=mn-1 nm-1 when m ≥1 and n ≥1, since fm,n,m+n-1 is the number of spanning trees in Km,n. In this paper, we give an algorithm for computing fm,n,h for general m,n,h. We implement this algorithm and use it to compute all non-zero fm,n,h when m ≤50 and n ≤50 in under 2 days.

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