Some Generalized Bipartite Ramsey Numbers Involving Short Cycles

Ernst J. Joubert

doi:10.1007/s00373-017-1761-z

Some Generalized Bipartite Ramsey Numbers Involving Short Cycles

Ernst J. Joubert

Mathematics and Applied Mathematics

Research output: Contribution to journal › Article › peer-review

9 Citations (Scopus)

Abstract

For bipartite graphs G₁, G₂, … , G_k, the bipartite Ramsey number b(G₁, G₂, … , G_k) is the least positive integer b so that any colouring of the edges of K_b _, _b with k colours will result in a copy of G_i in the ith colour for some i. In this paper, we will consider the bipartite Ramsey number b(C2t1,C2t2,…,C2tk), where t_i is an integer and 2 ≤ t_i≤ 4 , for all 1 ≤ i≤ k. In particular, we will show that b(C2t1,C2t2,…,C2tk)≤ k(t₁+ t₂+ ⋯ + t_k- k+ 1).

Original language	English
Pages (from-to)	433-448
Number of pages	16
Journal	Graphs and Combinatorics
Volume	33
Issue number	2
DOIs	https://doi.org/10.1007/s00373-017-1761-z
Publication status	Published - 1 Mar 2017

Keywords

Bipartite graph
Cycle
Ramsey

ASJC Scopus subject areas

Theoretical Computer Science
Discrete Mathematics and Combinatorics

Access to Document

10.1007/s00373-017-1761-z

Cite this

@article{03e9c038cf2e42ceb8fe9fdb39d5fe18,

title = "Some Generalized Bipartite Ramsey Numbers Involving Short Cycles",

abstract = "For bipartite graphs G1, G2, … , Gk, the bipartite Ramsey number b(G1, G2, … , Gk) is the least positive integer b so that any colouring of the edges of Kb , b with k colours will result in a copy of Gi in the ith colour for some i. In this paper, we will consider the bipartite Ramsey number b(C2t1,C2t2,…,C2tk), where ti is an integer and 2 ≤ ti≤ 4 , for all 1 ≤ i≤ k. In particular, we will show that b(C2t1,C2t2,…,C2tk)≤ k(t1+ t2+ ⋯ + tk- k+ 1).",

keywords = "Bipartite graph, Cycle, Ramsey",

author = "Joubert, \{Ernst J.\}",

note = "Publisher Copyright: {\textcopyright} 2017, Springer Japan.",

year = "2017",

month = mar,

day = "1",

doi = "10.1007/s00373-017-1761-z",

language = "English",

volume = "33",

pages = "433--448",

journal = "Graphs and Combinatorics",

issn = "0911-0119",

publisher = "Springer Japan",

number = "2",

}

TY - JOUR

T1 - Some Generalized Bipartite Ramsey Numbers Involving Short Cycles

AU - Joubert, Ernst J.

PY - 2017/3/1

Y1 - 2017/3/1

N2 - For bipartite graphs G1, G2, … , Gk, the bipartite Ramsey number b(G1, G2, … , Gk) is the least positive integer b so that any colouring of the edges of Kb , b with k colours will result in a copy of Gi in the ith colour for some i. In this paper, we will consider the bipartite Ramsey number b(C2t1,C2t2,…,C2tk), where ti is an integer and 2 ≤ ti≤ 4 , for all 1 ≤ i≤ k. In particular, we will show that b(C2t1,C2t2,…,C2tk)≤ k(t1+ t2+ ⋯ + tk- k+ 1).

AB - For bipartite graphs G1, G2, … , Gk, the bipartite Ramsey number b(G1, G2, … , Gk) is the least positive integer b so that any colouring of the edges of Kb , b with k colours will result in a copy of Gi in the ith colour for some i. In this paper, we will consider the bipartite Ramsey number b(C2t1,C2t2,…,C2tk), where ti is an integer and 2 ≤ ti≤ 4 , for all 1 ≤ i≤ k. In particular, we will show that b(C2t1,C2t2,…,C2tk)≤ k(t1+ t2+ ⋯ + tk- k+ 1).

KW - Bipartite graph

KW - Cycle

KW - Ramsey

UR - https://www.scopus.com/pages/publications/85009209247

U2 - 10.1007/s00373-017-1761-z

DO - 10.1007/s00373-017-1761-z

M3 - Article

AN - SCOPUS:85009209247

SN - 0911-0119

VL - 33

SP - 433

EP - 448

JO - Graphs and Combinatorics

JF - Graphs and Combinatorics

IS - 2

ER -

Some Generalized Bipartite Ramsey Numbers Involving Short Cycles

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this