Results 11 to 20 of about 1,368 (181)

Generalized Ramsey theory and decomposable properties of graphs

Discussiones Mathematicae Graph Theory, 1999
Summary: We translate Ramsey-type problems into the language of decomposable hereditary properties of graphs. We prove a distributive law for reducible and decomposable properties of graphs. Using it we establish some values of graph theoretical invariants of decomposable properties and show their correspondence to generalized Ramsey numbers.
Stefan A. Burr, Michael S. Jacobson, Peter Mihók, Gabriel Semanisin   +3 more
openaire   +2 more sources

Generalized Ramsey theory for graphs. II. Small diagonal numbers [PDF]

Proceedings of the American Mathematical Society, 1972
Consider a finite nonnull graph G with no loops or multiple edges and no isolated points. Its Ramsey number r (
Chvátal, Václav, Harary, Frank
openaire   +2 more sources

Generalization of Ramsey Number for Cycle with Pendant Edges

Mathematics
This paper explores various Ramsey numbers associated with cycles with pendant edges, including the classical Ramsey number, the star-critical Ramsey number, the Gallai–Ramsey number, and the star-critical Gallai–Ramsey number.
Jagjeet Jakhar, Monu Moun, Youngsoo Seol, Majeed Ahmad Yousif, Muhammad Amer Latif, Pshtiwan Othman Mohammed   +5 more
doaj   +2 more sources

Generalized ramsey theory for graphs, x: double stars [PDF]

Discrete Mathematics, 1979
AbstractThe double star S(n, m), where n ⩾ m ⩾ 0, is the graph consisting of the union of two stars K1,n and K1,m together with a line joining their centers. Its ramsey number r(S(n, m)) is the least number p such that there is a monochromatic copy of S(n, m) in any 2-coloring of the edges of Kp.
Grossman, Jerrold W., Harary, Frank, Klawe, Maria   +2 more
openaire   +3 more sources

Corrections : Generalized Ramsey Theory for Graphs V [PDF]

Bulletin of the London Mathematical Society, 1975
Peer Reviewed ; http://deepblue.lib.umich.edu/bitstream/2027.42/135328/1/blms0087 ...
Harary, Frank, Hell, Pavol
openaire   +4 more sources

Ramsey Theory

, 2022
The Ramsey number $R(r, b)$ is the least positive integer such that every edge 2-coloring of the complete graph $K_{R(r, b)}$ with colors red and blue either embeds a red $K_r$ or a blue $K_b$. We explore various methods to find lower bounds on $R(r,b)$,
Lai, David
core   +1 more source

Diagonal Forms, Linear Algebraic Methods and Ramsey-Type Problems [PDF]

, 2013
This thesis focuses mainly on linear algebraic aspects of combinatorics. Let N_t(H) be an incidence matrix with edges versus all subhypergraphs of a complete hypergraph that are isomorphic to H. Richard M.
Wong, Wing Hong Tony
core   +1 more source

Ramsey numbers for trees II [PDF]

, 2021
summary:Let $r(G_1, G_2)$ be the Ramsey number of the two graphs $G_1$ and $G_2$. For $n_1\ge n_2\ge 1$ let $S(n_1,n_2)$ be the double star given by $V(S(n_1,n_2))=\{v_0,v_1,\ldots ,v_{n_1},w_0$, $w_1,\ldots ,w_{n_2}\}$ and $E(S(n_1,n_2))=\{v_0v_1,\ldots
Sun, Zhi-Hong
core   +1 more source

Generalized Ramsey numbers for graphs [PDF]

, 2015
The thesis contains new contributions to Ramsey theory, in particular results that establish exact values of graph Ramsey numbers that were not known to ...
Zhang, Yanbo
core   +1 more source

Eye movements, not reaction times, reveal anticipatory attentional bias in childhood social anxiety disorder. [PDF]

J Child Psychol Psychiatry
Background Social anxiety disorder (SAD) is characterized by attentional biases that may contribute to its persistence. While adult models emphasize self‐focused and hypervigilant attention, there is limited understanding of how these processes operate in children. This study examined internal and external attentional biases in children with SAD during
Vietmeier N, Dietze N, Tuschen-Caffier B, Asbrand J.   +3 more
europepmc   +2 more sources