SLO

Search the repository

A- | A+ | Print

Query:	search in
	search in
	search in
	search in
Work type:	* old and bologna study programme
Language:
Search in:
Options:	Show only hits with full text
	Reset

1 - 2 / 2

Reinforcement learning for graph theory, II. Small Ramsey numbers
Mohammad Ghebleh, Salem Al-Yakoob, Ali Kanso, Dragan Stevanović, 2025, original scientific article

Abstract: We describe here how the recent Wagner’s approach for applying reinforcement learning to construct examples in graph theory can be used in the search for critical graphs for small Ramsey numbers. We illustrate this application by providing lower bounds for the small Ramsey numbers R(K_{2, 5}, K_{3, 5}), R(B₃, B₆) and R(B₄, B₅) and by improving the lower known bound for R(W₅, W₇).
Keywords: Ramsey number, critical graph, reinforcement learning, cross-entropy method
Published in RUP: 03.11.2025; Views: 842; Downloads: 7
Full text (291,40 KB)

On a conjecture of Erdős on size Ramsey number of star forests
Akbar Davoodi, Ramin Javadi, Azam Kamranian, Ghaffar Raeisi, 2025, original scientific article

Abstract: Given two graphs F_1 and F_2, their size Ramsey number, denoted by r̂(F_1, F_2), is the minimum number of edges of a graph G such that for any edge coloring of G by colors red and blue, G contains either a red copy of F1 or a blue copy of F2. In this paper, we deal with the size Ramsey number of star forests (disjoint union of stars) and following a conjecture by Burr, Erdős, Faudree, Rousseau, and Schelp in 1978, we determine the exact value of r̂(⊔_{i = 1}^s K_{1, ni}, ⊔_{i = 1}^t K_{1, mi}) in several cases including when either m_i’s and n_i’s are odd, or s = 1 or s = 2 and n_1 = n_2.
Keywords: size Ramsey number, star forest, Ramsey minimal graph
Published in RUP: 21.10.2025; Views: 2017; Downloads: 11
Full text (282,24 KB)

Search done in 0 sec.