Cycle decompositions III: Complete graphs and fixed length cycles

By M. Šajna. 2002

238 citations recorded by the source corpus.

Subfields: Computer Networks and Communications, Discrete Mathematics and Combinatorics, Electrical and Electronic Engineering

View Paper: https://www.semanticscholar.org/paper/89a2e596408837c02c94d4fa85d421c09ca01076

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computer Networks and Communications

1. Darryn E. Bryant
2. Daniel Horsley
3. Marco Buratti

In Discrete Mathematics and Combinatorics

1. Darryn E. Bryant
2. Daniel Horsley
3. Marco Buratti

In Electrical and Electronic Engineering

1. Darryn E. Bryant
2. Daniel Horsley
3. Marco Buratti

Citations in the corpus

• Rotational k‐cycle systems of order v < 3k; another proof of the existence of odd cycle systems (2003, background): “This condition was recently proven to be also sufficient by Alspach and Gavlas [1] in the case of k odd and by Šajna [18] in the case of k even.”
• Cycle decompositions V: Complete graphs into cycles of arbitrary lengths (2012, background): “Many of these focussed on the case of decompositions into cycles of uniform length [7, 8, 12, 14, 32, 34, 35, 45], and a complete solution in this case was eventually obtained [6, 46].”
• Cycle decompositions of complete multigraphs (2009, background): “1 has already been proven for the important case of =1 in [3, 24, 25], and for the case =2 in [4].”
• A survey on the existence of G‐Designs (2008, background): “The case m is odd was settled by Alspach and Gavlas [22] in 2001 and the case m is even was settled by Šajna [108] in Journal of Combinatorial Designs DOI 10.1002/jcd 2002.”