Results 11 to 20 of about 1,298 (200)
Two problems in graph Ramsey theory [PDF]
European Journal of Combinatorics, 2022 We study two problems in graph Ramsey theory. In the early 1970's, Erdős and O'Neil considered a generalization of Ramsey numbers. Given integers $n,k,s$ and $t$ with $n \ge k \ge s,t \ge 2$, they asked for the least integer $N=f_k(n,s,t)$ such that in any red-blue coloring of the $k$-subsets of $\{1, 2,\ldots, N\}$, there is a set of size $n$ such ...
Tuan Tran, Tran, Tuan
openaire +3 more sources
Landauer Principle and Einstein Synchronization of Clocks: Ramsey Approach [PDF]
EntropyWe introduce a synchronization procedure for clocks based on the Einstein–Landauer framework. Clocks are modeled as discrete, macroscopic devices operating at a thermal equilibrium temperature T.
Edward Bormashenko, Michael Nosonovsky
doaj +2 more sources
Graph Ramsey theory and the polynomial hierarchy [PDF]
Proceedings of the thirty-first annual ACM symposium on Theory of Computing, 1999 One of the usual ways to formulate Ramsey theory statements for graphs is by using arrowing notation. \(F\to (G,H)\) means that if the edges of \(F\) are colored red and blue, either a red \(G\) or a blue \(H\) must occur. \textit{S. A. Burr} [Algorithms Comb.
Schaefer, Marcus, Marcus Schaefer
openaire +2 more sources
Finite Induced Graph Ramsey Theory: On Partitions of Subgraphs
Journal of Combinatorial Theory, Series B, 1993 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
David S. Gunderson +2 more
openaire +3 more sources
Recent developments in graph Ramsey theory [PDF]
, 2015 54 ...
Conlon, David +2 more
openaire +5 more sources
Problems in extremal graph theory and Euclidean Ramsey theory.
, 2019 This thesis addresses problems of three types. The first type is finding extremal numbers for unions of graphs, each with a colour-critical edge (joint work with V. Nikiforov). In 1968, Simonovits found extremal numbers $ex(n,H)$ for graphs with a colour-critical edge for large $n$ (without specifying how large).
Tsaturian, Sergei
openaire +3 more sources
Results in Ramsey theory and extremal graph theory
In this thesis, we study several combinatorial problems in which we aim to find upper or lower bounds on a certain quantity relating to graphs. The first problem is in Ramsey theory, while the others are in extremal graph theory. In Chapter 2, which is joint work with Vojtěch Dvořák, we consider the Ramsey number $R(F_n)$ of the fan graph $F_n$, a ...
openaire +3 more sources
Topics in finite graph Ramsey theory
, 2008 For a positive integer $r$ and graphs $F$, $G$, and $H$, the graph Ramsey arrow notation $F \longrightarrow (G)^H_r$ means that for every $r$-colouring of the subgraphs of $F$ isomorphic to $H$, there exists a subgraph $G'$ of $F$ isomorphic to $G$ such that all the subgraphs of $G'$ isomorphic to $H$ are coloured the same.
Borgersen, Robert David
openaire +2 more sources
Gallai-Ramsey Numbers for Rainbow S3+S_3^ + and Monochromatic Paths
Discussiones Mathematicae Graph Theory, 2022 Motivated by Ramsey theory and other rainbow-coloring-related problems, we consider edge-colorings of complete graphs without rainbow copy of some fixed subgraphs.
Li Xihe, Wang Ligong
doaj +1 more source
Singular Turán Numbers and Worm-Colorings
Discussiones Mathematicae Graph Theory, 2022 A subgraph G of H is singular if the vertices of G either have the same degree in H or have pairwise distinct degrees in H. The largest number of edges of a graph on n vertices that does not contain a singular copy of G is denoted by TS(n, G).
Gerbner Dániel +3 more
doaj +1 more source