On the existence of nearly Kirkman triple systems with subsystems

Deng, Dameng; Rees, Rolf S.; Shen, Hao

doi:10.1007/s10623-007-9166-2

Cited by 9 publications

(2 citation statements)

References 8 publications

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“…Corollary 3.5 gives a powerful result in the case when k ≡ 2 (mod 4) and v ≡ m ≡ k (mod 2k). The case where k = 3 has been considered in [34,35,36] when v and m are both odd, and [18,19,20,22,37] when they are both even. However, the case when m and v have opposite parities appears to be completely open.…”

Section: Uniform Factorsmentioning

confidence: 99%

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On the minisymposium problem

et al. 2024

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The generalized Oberwolfach problem asks for a factorization of the complete graph K v into prescribed 2-factors and at most a 1-factor. When all 2-factors are pairwise isomorphic and v is odd, we have the classic Oberwolfach problem, which was originally stated as a seating problem: given v attendees at a conference with t circular tables such that the ith table seats a i people and * We thank the anonymous referees for their many useful suggestions that helped strongly improve this paper. † P. Danziger has received support from NSERC Discovery Grants RGPIN-2022-03816. ‡ B. Stevens recieved support from NSERC Discovery Grant RGPIN-2017-06392. § Corresponding author. T. Traetta has received support from GNSAGA of Istituto Nazionale di Alta Matematica.

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Section: Uniform Factorsmentioning

confidence: 99%

“…The case when m is odd and v is even seems to be the hardest. Even in the simplest case when k = 3, which has been well studied otherwise [18,19,20,22,34,35,36,37], the case with v and m having opposite parities has not been previously considered and remains open.…”

Section: Conclusion and Further Workmentioning

confidence: 99%

On the minisymposium problem

et al. 2024

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A complete solution to the infinite Oberwolfach problem

Costa

2020

J of Combinatorial Designs

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Let F be a 2‐regular graph of order v. The Oberwolfach problem, OP(F), asks for a 2‐factorization of the complete graph on v vertices in which each 2‐factor is isomorphic to F. In this paper, we give a complete solution to the Oberwolfach problem over infinite complete graphs, proving the existence of solutions that are regular under the action of a given involution free group G. We will also consider the same problem in the more general context of graphs F that are spanning subgraphs of an infinite complete graph double-struckK and we provide a solution when F is locally finite. Moreover, we characterize the infinite subgraphs L of F such that there exists a solution to OP(F) containing a solution to OP(L).

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Group Divisible Designs with Block Size Four and Type $$g^u b^1 (gu/2)^1$$

Forbes

2020

Graphs and Combinatorics

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On the existence of nearly Kirkman triple systems with subsystems

Cited by 9 publications

References 8 publications

On the minisymposium problem

On the minisymposium problem

A complete solution to the infinite Oberwolfach problem

Group Divisible Designs with Block Size Four and Type $$g^u b^1 (gu/2)^1$$

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