Zobrazeno 1 - 10
of 286
pro vyhledávání: '"Aharoni, Ron"'
We study simplicial complexes (hypergraphs closed under taking subsets) that are the intersection of a given number k of matroids. We prove bounds on their chromatic numbers (the minimum number of edges required to cover the ground set) and their lis
Externí odkaz:
http://arxiv.org/abs/2407.08789
A Young diagram $Y$ is called wide if every sub-diagram $Z$ formed by a subset of the rows of $Y$ dominates $Z'$, the conjugate of $Z$. A Young diagram $Y$ is called Latin if its squares can be assigned numbers so that for each $i$, the $i$th row is
Externí odkaz:
http://arxiv.org/abs/2311.17670
A pair $(A,B)$ of hypergraphs is called orthogonal if $|a \cap b|=1$ for every pair of edges $a \in A$ and $b \in B$. An orthogonal pair of hypergraphs is called a loom if each of its two members is the set of minimum covers of the other. Looms appea
Externí odkaz:
http://arxiv.org/abs/2309.03735
Autor:
Aharoni, Ron, Guo, He
We give a simple proof of a recent result of Gollin and Jo\'o: if a possibly infinite system of homogeneous linear equations $A\vec{x} = \vec{0}$, where $A = (a_{i, j})$ is an $I \times J$ matrix, has only the trivial solution, then there exists an i
Externí odkaz:
http://arxiv.org/abs/2301.10312
Autor:
Aharoni, Ron
This is a not-to-be-journal-published paper, aimed to serve as reference. It is a summary of the main ideas on the topic appearing in the title, and an opportunity to state correctly the main conjecture in the field.
Externí odkaz:
http://arxiv.org/abs/2206.02576
Autor:
Aharoni, Ron, Guo, He
Publikováno v:
Israel Journal of Mathematics 256 (2023), 1--8
Given a graph G and a coloring of its edges, a subgraph of G is called rainbow if its edges have distinct colors. The rainbow girth of an edge coloring of G is the minimum length of a rainbow cycle in G. A generalization of the famous Caccetta-Haggkv
Externí odkaz:
http://arxiv.org/abs/2110.14332
Publikováno v:
SIAM Journal on Discrete Mathematics 37 (2023), 1704--1714
The Caccetta-H\"aggkvist conjecture (denoted below CHC) states that the directed girth (the smallest length of a directed cycle) $dgirth(D)$ of a directed graph $D$ on $n$ vertices is at most $\lceil \frac{n}{\delta^+(D)}\rceil$, where $\delta^+(D)$
Externí odkaz:
http://arxiv.org/abs/2110.11183
Autor:
Aharoni, Ron, Briggs, Joseph
This is a survey paper on rainbow sets (another name for ``choice functions''). The main theme is the distinction between two types of choice functions: those having a large (in the sense of belonging to some specified filter, namely closed up set of
Externí odkaz:
http://arxiv.org/abs/2107.12881
A conjecture of the first two authors is that $n$ matchings of size $n$ in any graph have a rainbow matching of size $n-1$. We prove a lower bound of $\frac{2}{3}n-1$, improving on the trivial $\frac{1}{2}n$, and an analogous result for hypergraphs.
Externí odkaz:
http://arxiv.org/abs/2012.14992
A d-partite hypergraph is called *fractionally balanced* if there exists a non-negative, not identically zero, function on its edge set that has constant degrees in each vertex side. Using a topological version of Hall's theorem we prove lower bounds
Externí odkaz:
http://arxiv.org/abs/2011.01053