Zobrazeno 1 - 10
of 28
pro vyhledávání: '"Tommaso Traetta"'
Publikováno v:
Discrete Mathematics. 342:2213-2222
The Hamilton–Waterloo Problem HWP ( v ; m , n ; α , β ) asks for a 2-factorization of the complete graph K v or K v − I , the complete graph with the edges of a 1-factor removed, into α C m -factors and β C n -factors, where 3 ≤ m n . In th
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::c3fbffc6069e275db46e0f427d4436a7
https://doi.org/10.1016/j.disc.2019.04.013
https://doi.org/10.1016/j.disc.2019.04.013
Autor:
Simone Costa, Tommaso Traetta
The existence of $1$-factorizations of an infinite complete equipartite graph $K_m[n]$ (with $m$ parts of size $n$) admitting a vertex-regular automorphism group $G$ is known only when $n=1$ and $m$ is countable (that is, for countable complete graph
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::2c416e50b2cae551c85501bd6f3ac4e1
http://arxiv.org/abs/2106.09468
http://arxiv.org/abs/2106.09468
Publikováno v:
Università degli Studi di Brescia-IRIS
The Oberwolfach Problem $OP(F)$ -- posed by Gerhard Ringel in 1967 -- is a paradigmatic Combinatorial Design problem asking whether the complete graph $K_v$ decomposes into edge-disjoint copies of a $2$-regular graph $F$ of order $v$. In this paper,
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::0d53f041fa26717d98148ae03fdc784d
http://hdl.handle.net/11379/538196
http://hdl.handle.net/11379/538196
A $k$-cycle with a pendant edge attached to each vertex is called a $k$-sun. The existence problem for $k$-sun decompositions of $K_v$, with $k$ odd, has been solved only when $k=3$ or $5$. By adapting a method used by Hoffmann, Lindner and Rodger to
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::87d1c88aab607ddc2ebb8d50a56907fd
http://hdl.handle.net/11391/1501572
http://hdl.handle.net/11391/1501572
Kirkman triple systems (KTSs) are among the most popular combinatorial designs and their existence has been settled a long time ago. Yet, in comparison with Steiner triple systems, little is known about their automorphism groups. In particular, there
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::f99011bb84ae3ebb457192a2753d28ae
In this paper, we study the existence problem for cyclic $\ell$-cycle decompositions of the graph $K_m[n]$, the complete multipartite graph with $m$ parts of size $n$, and give necessary and sufficient conditions for their existence in the case that
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::a50f3132006582d97123037babb4eb1b
http://hdl.handle.net/11379/537916
http://hdl.handle.net/11379/537916
Publikováno v:
Journal of Combinatorial Designs. 25:258-287
Given nonnegative integers v,m,n,α,β, the Hamilton–Waterloo problem asks for a factorization of the complete graph Kv into α Cm-factors and β Cn-factors. Without loss of generality, we may assume that n≥m. Clearly, v odd, n,m≥3, m∣v, n∣
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::3794dbcc64f55c4be7951f75c7b8f79c
https://doi.org/10.1002/jcd.21552
https://doi.org/10.1002/jcd.21552
Publikováno v:
Journal of Combinatorial Designs. 25:197-230
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::77612d6f14f5bddbb6e4b7b0006b8c2c
https://doi.org/10.1002/jcd.21523
https://doi.org/10.1002/jcd.21523
Let K v ∗ denote the complete graph K v if v is odd and K v − I , the complete graph with the edges of a 1-factor removed, if v is even. Given non-negative integers v , M , N , α , β , the Hamilton–Waterloo problem asks for a 2-factorization
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::9b83216c44531625f827d718a515cce9
http://hdl.handle.net/11379/515687
http://hdl.handle.net/11379/515687
Let Kv∗ denote the complete graph Kv if v is odd and Kv−I, the complete graph with the edges of a 1-factor removed, if v is even. Given nonnegative integers v,M,N,α,β, the Hamilton–Waterloo problem asks for a 2-factorization of Kv∗ into α
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::94c747ab8e62f0eb0989b06c6a45eaad
http://hdl.handle.net/11379/515686
http://hdl.handle.net/11379/515686