| 1. |
- Casselgren, Carl Johan, et al.
(författare)
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Restricted extension of sparse partial edge colorings of hypercubes
- 2020
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Ingår i: Discrete Mathematics. - : ELSEVIER. - 0012-365X .- 1872-681X. ; 343:11
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Tidskriftsartikel (refereegranskat)abstract
- We consider the following type of question: Given a partial proper d-edge coloring of the d-dimensional hypercube Qd, and lists of allowed colors for the non-colored edges of Qd, can we extend the partial coloring to a proper d-edge coloring using only colors from the lists? We prove that this question has a positive answer in the case when both the partial coloring and the color lists satisfy certain sparsity conditions. (C) 2020 Elsevier B.V. All rights reserved.
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| 2. |
- Janson, Svante, 1955-
(författare)
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A graphon counter example
- 2020
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Ingår i: Discrete Mathematics. - : ELSEVIER. - 0012-365X .- 1872-681X. ; 343:6
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Tidskriftsartikel (refereegranskat)abstract
- We give an example of a graphon such that there is no equivalent graphon with a degree function that is (weakly) increasing.
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| 3. |
- Kokkala, Janne, et al.
(författare)
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Kirkman triple systems with subsystems
- 2020
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Ingår i: Discrete Mathematics. - : Elsevier. - 0012-365X .- 1872-681X. ; 343:9
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Tidskriftsartikel (refereegranskat)abstract
- A Steiner triple system of order v, STS(v), together with a resolution of its blocks is called a Kirkman triple system of order v, KTS(v). A KTS(v) exists if and only if v≡3(mod6). The smallest order for which the KTS(v) have not been classified is v=21, which is also the smallest order for which the existence of a doubly resolvable STS(v) is open. Here, KTS(21) with STS(7) and STS(9) subsystems are classified, leading to more than 13 million KTS(21). In this process, systems missing from an earlier classification of KTS(21) with nontrivial automorphisms are encountered, so such a classification is redone.
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