Zobrazeno 1 - 10
of 333
pro vyhledávání: '"Allan Lo"'
This volume contains eight survey articles based on the invited lectures given at the 27th British Combinatorial Conference, held at the University of Birmingham in July 2019. This biennial conference is a well-established international event, with s
Publikováno v:
Memoirs of the American Mathematical Society. 284
We solve the existence problem for F F -designs for arbitrary r r -uniform hypergraphs F F . This implies that given any r r -uniform hypergraph F F , the trivially necessary divisibility conditions are sufficient to guarantee a decomposition of any
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::fd2528baf8a79eccd4d109d9b4425e7e
https://doi.org/10.1090/memo/1406
https://doi.org/10.1090/memo/1406
Autor:
A. Nicholas Day, Allan Lo
Publikováno v:
European Journal of Combinatorics. 110:103625
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::ebca29d0a083ab28062b72316bee678b
https://doi.org/10.1016/j.ejc.2022.103625
https://doi.org/10.1016/j.ejc.2022.103625
Publikováno v:
Combinatorica. 40:363-403
A famous theorem of Kirkman says that there exists a Steiner triple system of order n if and only if n ≡ 1,3 mod 6. In 1973, Erdős conjectured that one can find so-called ‘sparse’ Steiner triple systems. Roughly speaking, the aim is to have at
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::4155cf48678f4b28d9054138df405107
https://doi.org/10.1007/s00493-019-4084-2
https://doi.org/10.1007/s00493-019-4084-2
Autor:
Louis DeBiasio, Allan Lo
Publikováno v:
SIAM Journal on Discrete Mathematics. 33:1503-1520
A branch vertex in a tree is a vertex of degree at least three. We prove that, for all $s\geq 1$, every connected graph on $n$ vertices with minimum degree at least $(\frac{1}{s+3}+o(1))n$ contains a spanning tree having at most $s$ branch vertices.
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::51d71f9f88d3f936d8128b99230deb91
https://doi.org/10.1137/17m1152759
https://doi.org/10.1137/17m1152759
Autor:
Vincent Pfenninger, Allan Lo
Publikováno v:
Trends in Mathematics ISBN: 9783030838225
A 4-uniform tight cycle is a 4-uniform hypergraph with a cyclic ordering of its vertices such that its edges are precisely the sets of 4 consecutive vertices in that ordering. We prove that the Ramsey number for the 4-uniform tight cycle on 4n vertic
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::0061b45478de5341d49117bcbd6d1f2e
https://doi.org/10.1007/978-3-030-83823-2_69
https://doi.org/10.1007/978-3-030-83823-2_69
Publikováno v:
Trends in Mathematics ISBN: 9783030838225
In 1976, Alspach, Mason, and Pullman conjectured that any tournament T of even order can be decomposed into exactly \(\mathrm{ex}(T)\) paths, where \(\mathrm{ex}(T) = \frac{1}{2}\sum _{v\in V(T)}|d_T^+(v)-d_T^-(v)|\). We prove this conjecture for all
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::ec989160a96728bb56dd0148cbcf8119
https://doi.org/10.1007/978-3-030-83823-2_31
https://doi.org/10.1007/978-3-030-83823-2_31
Autor:
Allan Lo, Vincent Pfenninger
A $k$-uniform tight cycle is a $k$-uniform hypergraph with a cyclic ordering of its vertices such that its edges are all the sets of size $k$ formed by $k$ consecutive vertices in the ordering. We prove that every red-blue edge-coloured $K_n^{(4)}$ c
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::78c3038c7806b5b620d0b32fe24fa6e0
http://arxiv.org/abs/2012.08875
http://arxiv.org/abs/2012.08875
Autor:
Allan Lo
Publikováno v:
Journal of Graph Theory. 90:416-442
Let $G$ be an edge-coloured graph. The minimum colour degree $\delta^c(G)$ of $G$ is the largest integer $k$ such that, for every vertex $v$, there are at least $k$ distinct colours on edges incident to $v$. We say that $G$ is properly coloured if no
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::592a17d20d4da07fc9040e1e6aa2df30
https://doi.org/10.1002/jgt.22405
https://doi.org/10.1002/jgt.22405