Zobrazeno 1 - 10
of 116
pro vyhledávání: '"Darryn BRYANT"'
Publikováno v:
Journal of Combinatorial Theory, Series B. 135:1-15
We prove that a complete multipartite graph K with n > 1 vertices and m edges can be decomposed into edge-disjoint Hamilton paths if and only if m n − 1 is an integer and the maximum degree of K is at most 2 m n − 1 .
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::b4999b853d2303676d39c8c4b1530cc8
https://doi.org/10.1016/j.jctb.2018.07.006
https://doi.org/10.1016/j.jctb.2018.07.006
Publikováno v:
Journal of Combinatorial Designs. 26:595-615
The notion of uniformity, as in uniform 1 -factorisations, extends naturally to graph decompositions generally. The existence of uniform decompositions of complete multigraphs into cycles is investigated and some connections with families of classica
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::403a2b2b2dd572c36940a36d02cebace
https://doi.org/10.1002/jcd.21630
https://doi.org/10.1002/jcd.21630
Publikováno v:
Journal of Combinatorial Theory, Series B. 129:79-106
We establish necessary and sufficient conditions for the existence of a decomposition of a complete multigraph into edge-disjoint cycles of specified lengths, or into edge-disjoint cycles of specified lengths and a perfect matching.
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::3070b8318f39a5940bf616f2e8ce1a12
https://doi.org/10.1016/j.jctb.2017.09.005
https://doi.org/10.1016/j.jctb.2017.09.005
A partial Steiner triple system of order $u$ is a pair $(U,\mathcal{A})$ where $U$ is a set of $u$ elements and $\mathcal{A}$ is a set of triples of elements of $U$ such that any two elements of $U$ occur together in at most one triple. If each pair
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::4dd85337c5bb5ed42b2855fed880e1d6
http://arxiv.org/abs/1911.02196
http://arxiv.org/abs/1911.02196
Publikováno v:
Ars mathematica contemporanea
Scopus-Elsevier
Scopus-Elsevier
Various results on factorisations of complete graphs into circulant graphs and on 2-factorisations of these circulant graphs are proved. As a consequence, a number of new results on the Oberwolfach Problem are obtained. For example, a complete soluti
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::4508769f13f7da7ee18b844005b5a9f6
https://doi.org/10.26493/1855-3974.770.150
https://doi.org/10.26493/1855-3974.770.150
Autor:
Matthew Dean, Darryn Bryant
Publikováno v:
Journal of Combinatorial Theory, Series B. 114:237-246
It is shown that there are infinitely many connected vertex-transitive graphs that have no Hamilton decomposition, including infinitely many Cayley graphs of valency 6, and including Cayley graphs of arbitrarily large valency.
Comment: This vers
Comment: This vers
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::8c98f43e5e722d754bc7471fe8286d41
https://doi.org/10.1016/j.jctb.2015.05.007
https://doi.org/10.1016/j.jctb.2015.05.007
Autor:
Darryn Bryant, Padraig Ó Catháin
Publikováno v:
Linear Algebra and its Applications. 475:134-150
For any rational number h and all sufficiently large n we give a deterministic construction for an n × ⌊ h n ⌋ compressed sensing matrix with ( l 1 , t ) -recoverability where t = O ( n ) . Our method uses pairwise balanced designs and complex H
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::82744df688ee14e08c71faa2b489900a
https://doi.org/10.1016/j.laa.2015.02.010
https://doi.org/10.1016/j.laa.2015.02.010
Publikováno v:
University of Queensland
In contrast with Kotzig's result that the line graph of a $3$-regular graph $X$ is Hamilton decomposable if and only if $X$ is Hamiltonian, we show that for each integer $k\geq 4$ there exists a simple non-Hamiltonian $k$-regular graph whose line gra
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::dbde85a66a0352b163b715ad2ae06b60
http://arxiv.org/abs/1710.06037
http://arxiv.org/abs/1710.06037
It is conjectured that every Steiner triple system of order $v \neq 7$ has chromatic index at most $(v+3)/2$ when $v \equiv 3 \pmod{6}$ and at most $(v+5)/2$ when $v \equiv 1 \pmod{6}$. Herein, we construct a Steiner triple system of order $v$ with c
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::1c0542cc1f63fdb965e257653086678c
Autor:
Darryn Bryant, Nicholas J. Cavenagh
Publikováno v:
Journal of Graph Theory. 79:167-177
If a graph G decomposes into edge-disjoint 4-cycles, then each vertex of G has even degree and 4 divides the number of edges in G. It is shown that these obvious necessary conditions are also sufficient when G is any simple graph having minimum degre
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::7ac584cde79d92d06b5966704c728472
https://doi.org/10.1002/jgt.21816
https://doi.org/10.1002/jgt.21816