1University of Illinois at Urbana-Champaign, Urbana, IL 61801 and Sobolev Institute of Mathematics, Novosibirsk 630090, Russia 2University of Califonia, San Diego, La Jolla, CA 92093, USA and University of Illinois at Urbana-Champaign, Urbana, IL 61801, USA 3University of Illinois at Urbana-Champaign, Urbana, IL 61801, USA
The electronic journal of combinatorics, Tome 28 (2021) no. 1
A hypergraph $\mathcal H$ is super-pancyclic if for each $A \subseteq V(\mathcal H)$ with $|A| \geqslant 3$, $\mathcal H$ contains a Berge cycle with base vertex set $A$. We present two natural necessary conditions for a hypergraph to be super-pancyclic, and show that in several classes of hypergraphs these necessary conditions are also sufficient. In particular, they are sufficient for every hypergraph $\mathcal H$ with $ \delta(\mathcal H)\geqslant \max\{|V(\mathcal H)|, \frac{|E(\mathcal H)|+10}{4}\}$. We also consider super-cyclic bipartite graphs: those are $(X,Y)$-bigraphs $G$ such that for each $A \subseteq X$ with $|A| \geqslant 3$, $G$ has a cycle $C_A$ such that $V(C_A)\cap X=A$. Such graphs are incidence graphs of super-pancyclic hypergraphs, and our proofs use the language of such graphs.
Alexandr Kostochka
1
;
Mikhail Lavrov
;
Ruth Luo
2
;
Dara Zirlin
3
1
University of Illinois at Urbana-Champaign, Urbana, IL 61801 and Sobolev Institute of Mathematics, Novosibirsk 630090, Russia
2
University of Califonia, San Diego, La Jolla, CA 92093, USA and University of Illinois at Urbana-Champaign, Urbana, IL 61801, USA
3
University of Illinois at Urbana-Champaign, Urbana, IL 61801, USA
@article{10_37236_9683,
author = {Alexandr Kostochka and Mikhail Lavrov and Ruth Luo and Dara Zirlin},
title = {Conditions for a bigraph to be super-cyclic},
journal = {The electronic journal of combinatorics},
year = {2021},
volume = {28},
number = {1},
doi = {10.37236/9683},
zbl = {1456.05088},
url = {http://geodesic.mathdoc.fr/articles/10.37236/9683/}
}
TY - JOUR
AU - Alexandr Kostochka
AU - Mikhail Lavrov
AU - Ruth Luo
AU - Dara Zirlin
TI - Conditions for a bigraph to be super-cyclic
JO - The electronic journal of combinatorics
PY - 2021
VL - 28
IS - 1
UR - http://geodesic.mathdoc.fr/articles/10.37236/9683/
DO - 10.37236/9683
ID - 10_37236_9683
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%0 Journal Article
%A Alexandr Kostochka
%A Mikhail Lavrov
%A Ruth Luo
%A Dara Zirlin
%T Conditions for a bigraph to be super-cyclic
%J The electronic journal of combinatorics
%D 2021
%V 28
%N 1
%U http://geodesic.mathdoc.fr/articles/10.37236/9683/
%R 10.37236/9683
%F 10_37236_9683
Alexandr Kostochka; Mikhail Lavrov; Ruth Luo; Dara Zirlin. Conditions for a bigraph to be super-cyclic. The electronic journal of combinatorics, Tome 28 (2021) no. 1. doi: 10.37236/9683
