scholarly journals Resolvable gregarious cycle decompositions of complete equipartite graphs

2008 ◽  
Vol 308 (13) ◽  
pp. 2844-2853 ◽  
Author(s):  
Elizabeth J. Billington ◽  
D.G. Hoffman ◽  
C.A. Rodger
Keyword(s):  
Cycle Decompositions ◽  
Equipartite Graphs

scholarly journals Path and cycle decompositions of complete equipartite graphs: Four parts

2009 ◽  
Vol 309 (10) ◽  
pp. 3061-3073 ◽  
Author(s):  
Elizabeth J. Billington ◽  
Nicholas J. Cavenagh ◽  
Benjamin R. Smith
Keyword(s):  
Cycle Decompositions ◽  
Equipartite Graphs

scholarly journals Path and cycle decompositions of complete equipartite graphs: 3 and 5 parts

2010 ◽  
Vol 310 (2) ◽  
pp. 241-254 ◽  
Author(s):  
Elizabeth J. Billington ◽  
Nicholas J. Cavenagh ◽  
Benjamin R. Smith
Keyword(s):  
Cycle Decompositions ◽  
Equipartite Graphs

scholarly journals Some Gregarious Cycle Decompositions of Complete Equipartite Graphs

10.37236/224 ◽  
2009 ◽  
Vol 16 (1) ◽  
Author(s):  
Benjamin R. Smith
Keyword(s):  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Cycle Decomposition ◽  
Multipartite Graph ◽  
Necessary And Sufficient ◽  
Cycle Decompositions ◽  
Equipartite Graphs

A $k$-cycle decomposition of a multipartite graph $G$ is said to be gregarious if each $k$-cycle in the decomposition intersects $k$ distinct partite sets of $G$. In this paper we prove necessary and sufficient conditions for the existence of such a decomposition in the case where $G$ is the complete equipartite graph, having $n$ parts of size $m$, and either $n\equiv 0,1\pmod{k}$, or $k$ is odd and $m\equiv 0\pmod{k}$. As a consequence, we prove necessary and sufficient conditions for decomposing complete equipartite graphs into gregarious cycles of prime length.

scholarly journals On Hamilton cycle decompositions of the tensor product of complete graphs

2003 ◽  
Vol 268 (1-3) ◽  
pp. 49-58 ◽  
Author(s):  
R. Balakrishnan ◽  
J.-C. Bermond ◽  
P. Paulraja ◽  
M.-L. Yu
Keyword(s):  
Tensor Product ◽  
Hamilton Cycle ◽  
Complete Graphs ◽  
Cycle Decompositions

scholarly journals Some equitably 3-colourable cycle decompositions

2004 ◽  
Vol 284 (1-3) ◽  
pp. 21-35 ◽  
Author(s):  
Peter Adams ◽  
Darryn Bryant ◽  
James Lefevre ◽  
Mary Waterhouse
Keyword(s):  
Cycle Decompositions

Orthogonally Resolvable Cycle Decompositions

2014 ◽  
Vol 23 (8) ◽  
pp. 328-351 ◽  
Author(s):  
A. Burgess ◽  
P. Danziger ◽  
E. Mendelsohn ◽  
B. Stevens
Keyword(s):  
Cycle Decompositions

On tight 6-cycle decompositions of complete 3-uniform hypergraphs

2022 ◽  
Vol 345 (2) ◽  
pp. 112676
Author(s):  
Matthew Akin ◽  
Ryan C. Bunge ◽  
Saad I. El-Zanati ◽  
Joshua Hamilton ◽  
Brittany Kolle ◽  
...  
Keyword(s):  
Uniform Hypergraphs ◽  
Cycle Decompositions
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