Tur\'an problems for Edge-ordered graphs.
@article{Gerbner2020TuranPF, title={Tur\'an problems for Edge-ordered graphs.}, author={D{\'a}niel Gerbner and Abhishek Methuku and D{\'a}niel T. Nagy and Domotor P'alvolgyi and G{\'a}bor Tardos and M{\'a}t{\'e} Vizer}, journal={arXiv: Combinatorics}, year={2020} }
In this paper we initiate a systematic study of the Turan problem for edge-ordered graphs. A simple graph is called $\textit{edge-ordered}$, if its edges are linearly ordered. An isomorphism between edge-ordered graphs must respect the edge-order. A subgraph of an edge-ordered graph is itself an edge-ordered graph with the induced edge-order. We say that an edge-ordered graph $G$ $\textit{avoids}$ another edge-ordered graph $H$, if no subgraph of $G$ is isomorphic to $H$.
The $\textit{Turan…
2 Citations
Saturation of Ordered Graphs
- Mathematics
- 2022
Recently, the saturation problem of 0-1 matrices gained a lot of attention. This problem can be regarded as a saturation problem of ordered bipartite graphs. Motivated by this, we initiate the study…
The number of tangencies between two families of curves
- MathematicsArXiv
- 2021
We prove that the number of tangencies between the members of two families, each of which consists of n pairwise disjoint curves, can be as large as Ω( n 4 / 3 ) . We show that from a conjecture…
References
SHOWING 1-10 OF 42 REFERENCES
Increasing Paths in Edge-Ordered Graphs: The Hypercube and Random Graph
- MathematicsElectron. J. Comb.
- 2016
Borders on f are given on the hypercube and the random graph G(n,p) for which the parameter f was first studied for G=K_n and has subsequently been studied for other families of graphs.
On edge‐ordered Ramsey numbers
- MathematicsRandom Struct. Algorithms
- 2020
It is proved that for every edge-ordered graph $H$ on $n$ vertices, the authors have $r_{edge}(H;q) \leq 2^{c^qn^{2q-2}\log^q n}$, where $c$ is an absolute constant.
Monotone Paths in Dense Edge-Ordered Graphs
- Mathematics
- 2015
The altitude of a graph $G$, denoted $f(G)$, is the largest integer $k$ such that under each ordering of $E(G)$, there exists a path of length $k$ which traverses edges in increasing order. In 1971,…
Non-crossing monotone paths and binary trees in edge-ordered complete geometric graphs
- MathematicsActa Mathematica Hungarica
- 2021
An edge-ordered graph is a graph with a total ordering of its edges. A path $P=v_1v_2\ldots v_k$ in an edge-ordered graph is called increasing if $(v_iv_{i+1}) > (v_{i+1}v_{i+2})$ for all $i =…
Statistics of orderings
- Mathematics
- 2017
In this paper, we study a Ramsey type problems dealing with the number of ordered subgraphs present in an arbitrary ordering of a larger graph. Our first result implies that for every vertex ordered…
Bipartite Tur\'an problems for ordered graphs
- Mathematics
- 2019
A zero-one matrix $M$ contains a zero-one matrix $A$ if one can delete some rows and columns of $M$, and turn some 1-entries into 0-entries such that the resulting matrix is $A$. The extremal number…
Forbidden paths and cycles in ordered graphs and matrices
- Mathematics
- 2006
At most how many edges can an ordered graph ofn vertices have if it does not contain a fixed forbidden ordered subgraphH? It is not hard to give an asymptotically tight answer to this question,…
Increasing Hamiltonian paths in random edge orderings
- MathematicsRandom Struct. Algorithms
- 2016
The surprising result that in the random setting, S(f) often takes its maximum possible value of n – 1 (visiting all of the vertices with an increasing Hamiltonian path) is discovered, suggesting that this Hamiltonian (or near-Hamiltonian) phenomenon may hold asymptotically almost surely.
Nearly-linear monotone paths in edge-ordered graphs
- Mathematics
- 2018
How long a monotone path can one always find in any edge-ordering of the complete graph K n ? This appealing question was first asked by Chvátal and Komlós in 1971, and has since attracted the…