Bipartite Ramsey numbers involving stars, stripes and trees | Zendy

Michalis Christou | Zendy; Costas S. Iliopoulos | Zendy; Mirka Miller | Zendy

AI Assistant Blog Pricing

Home ZAIA Blog

Open Access

Bipartite Ramsey numbers involving stars, stripes and trees

Author(s) -

Michalis Christou,

Costas S. Iliopoulos,

Mirka Miller

Publication year - 2013

Publication title -

electronic journal of graph theory and applications

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.443

H-Index - 5

ISSN - 2338-2287

DOI - 10.5614/ejgta.2013.1.2.2

Subject(s) - bipartite graph , combinatorics , complete bipartite graph , monochromatic color , ramsey's theorem , mathematics , edge transitive graph , graph , complete graph , stars , discrete mathematics , graph power , line graph , physics , astrophysics , optics

The Ramsey number R(m, n) is the smallest integer p such that any blue-red colouring of the edges of the complete graph Kp forces the appearance of a blue Km or a red Kn. Bipartite Ramsey problems deal with the same questions but the graph explored is the complete bipartite graph instead of the complete graph. We consider special cases of the bipartite Ramsey problem. More specifically we investigate the appearance of simpler monochromatic graphs such as stripes, stars and trees under a 2-colouring of the edges of a bipartite graph. We give the Ramsey numbers Rb(mP2, nP2), Rb(Tm, Tn), Rb(Sm, nP2), Rb(Tm, nP2) and Rb(Sm, Tn).

The content you want is available to Zendy users.

Already have an account? Click here to sign in.

Having issues? You can contact us here

Accelerating Research