Title of article :
Bipartite Ramsey numbers involving stars, stripes and trees
Author/Authors :
Christou, Michalis King’s College London - Department of Informatics, UK , Iliopoulos, Costas S. Curtin University - Digital Ecosystems Business Intelligence Institute, Australia , Iliopoulos, Costas S. King’s College London - Department of Informatics, UK , Miller, Mirka University of Newcastle - School of Mathematical and Physical Sciences, Australia , Miller, Mirka University of West Bohemia - Department of Mathematics, Czech Republic
Abstract :
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 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).
Keywords :
bipartite Ramsey theory , stars , stripes , trees
Journal title :
Electronic Journal of Graph Theory and Applications (EJGTA)
Journal title :
Electronic Journal of Graph Theory and Applications (EJGTA)
