• Corpus ID: 209832444

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

Figures from this paper

Saturation of Ordered Graphs
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
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
TLDR
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
TLDR
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
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
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
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
On the Turán number of ordered forests
Bipartite Tur\'an problems for ordered graphs
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
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
TLDR
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
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
...
1
2
3
4
5
...