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IEICE TRANSACTIONS on Fundamentals

Open Access
Ramsey Numbers of Trails

Masatoshi OSUMI

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Summary :

We initiate the study of Ramsey numbers of trails. Let k≥2 be a positive integer. The Ramsey number of trails with k vertices is defined as the the smallest number n such that for every graph H with n vertices, H or the complete H contains a trail with k vertices. We prove that the Ramsey number of trails with k vertices is at most k and at least 2√k+Θ(1). This improves the trivial upper bound of ⌊3k/2⌋-1.

Publication
IEICE TRANSACTIONS on Fundamentals Vol.E105-A No.9 pp.1235-1240
Publication Date
2022/09/01
Publicized
2022/03/24
Online ISSN
1745-1337
DOI
10.1587/transfun.2021DMP0003
Type of Manuscript
Special Section PAPER (Special Section on Discrete Mathematics and Its Applications)
Category
Graphs and Networks

Authors

Masatoshi OSUMI
  the University of Electro-Communications

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