Zobrazeno 1 - 10
of 224
pro vyhledávání: '"Kaiser, Tomáš"'
Autor:
Hylasová, Karolína, Kaiser, Tomáš
The shrinking operation converts a hypergraph into a graph by choosing, from each hyperedge, two endvertices of a corresponding graph edge. A hypertree is a hypergraph which can be shrunk to a tree on the same vertex set. Klimo\v{s}ov\'{a} and Thomas
Externí odkaz:
http://arxiv.org/abs/2405.02049
Strengthening the classical concept of Steiner trees, West and Wu [J. Combin. Theory Ser. B 102 (2012), 186--205] introduced the notion of a $T$-connector in a graph $G$ with a set $T$ of terminals. They conjectured that if the set $T$ is $3k$-edge-c
Externí odkaz:
http://arxiv.org/abs/2308.07218
Autor:
Kaiser, Tomáš, Stehlík, Matěj
Pachner proved that all closed combinatorially equivalent combinatorial manifolds can be transformed into each other by a finite sequence of bistellar moves. We prove an analogue of Pachner's theorem for combinatorial manifolds with a free Z2-action,
Externí odkaz:
http://arxiv.org/abs/2308.07103
We answer a question posed by T. Gallai in 1969 concerning criticality in Sperner's lemma, listed as Problem 9.14 in the collection of Jensen and Toft [Graph coloring problems, John Wiley & Sons, Inc., New York, 1995]. Sperner's lemma states that if
Externí odkaz:
http://arxiv.org/abs/2301.03420
Recently, it was proved by B\'erczi and Schwarcz that the problem of factorizing a matroid into rainbow bases with respect to a given partition of its ground set is algorithmically intractable. On the other hand, many special cases were left open. We
Externí odkaz:
http://arxiv.org/abs/2206.10322
Autor:
Kaiser, Tomáš, Vrána, Petr
We prove that every 52-connected line graph of a rank 3 hypergraph is Hamiltonian. This is the first result of this type for hypergraphs of bounded rank other than ordinary graphs.
Externí odkaz:
http://arxiv.org/abs/2201.13115
An independent transversal of a graph $G$ with a vertex partition $\mathcal P$ is an independent set of $G$ intersecting each block of $\mathcal P$ in a single vertex. Wanless and Wood proved that if each block of $\mathcal P$ has size at least $t$ a
Externí odkaz:
http://arxiv.org/abs/2106.15175
Autor:
Kaiser, Tomáš, Stehlík, Matěj
Publikováno v:
Journal of Combinatorial Theory, Series B 152: 453-482, 2022
We give a simple combinatorial description of an $(n-2k+2)$-chromatic edge-critical subgraph of the Schrijver graph $\mathrm{SG}(n,k)$, itself an induced vertex-critical subgraph of the Kneser graph $\mathrm{KG}(n,k)$. This extends the main result of
Externí odkaz:
http://arxiv.org/abs/2007.09204