• 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}
}
• Published 3 January 2020
• Mathematics
• arXiv: Combinatorics
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 $\textit{Turan… 2 Citations ## Figures from this paper Saturation of Ordered Graphs • Mathematics • 2022 Recently, the saturation problem of 0-1 matrices gained a lot of attention. This problem can be regarded as a saturation problem of ordered bipartite graphs. Motivated by this, we initiate the study The number of tangencies between two families of curves • Mathematics ArXiv • 2021 We prove that the number of tangencies between the members of two families, each of which consists of n pairwise disjoint curves, can be as large as Ω( n 4 / 3 ) . We show that from a conjecture ## References SHOWING 1-10 OF 42 REFERENCES Increasing Paths in Edge-Ordered Graphs: The Hypercube and Random Graph • Mathematics Electron. J. Comb. • 2016 Borders on f are given on the hypercube and the random graph G(n,p) for which the parameter f was first studied for G=K_n and has subsequently been studied for other families of graphs. On edge‐ordered Ramsey numbers • Mathematics Random Struct. Algorithms • 2020 It is proved that for every edge-ordered graph$H$on$n$vertices, the authors have$r_{edge}(H;q) \leq 2^{c^qn^{2q-2}\log^q n}$, where$c$is an absolute constant. Monotone Paths in Dense Edge-Ordered Graphs The altitude of a graph$G$, denoted$f(G)$, is the largest integer$k$such that under each ordering of$E(G)$, there exists a path of length$k$which traverses edges in increasing order. In 1971, Non-crossing monotone paths and binary trees in edge-ordered complete geometric graphs • Mathematics Acta Mathematica Hungarica • 2021 An edge-ordered graph is a graph with a total ordering of its edges. A path$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 =
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