Ramsey numbers for degree monotone paths

Yair Caro; Raphael Yuster; Christina Zarb

doi:10.1016/j.disc.2016.07.025

Ramsey numbers for degree monotone paths

Yair Caro, Raphael Yuster, Christina Zarb

Department of Mathematics

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

Abstract

A path v₁,v₂,…,v_m in a graph G is degree-monotone if deg(v₁)≤deg(v₂)≤⋯≤deg(v_m) where deg(v_i) is the degree of v_i in G. Longest degree-monotone paths have been studied in several recent papers. Here we consider the Ramsey type problem for degree monotone paths. Denote by M_k(m) the minimum number M such that for all n≥M, in any k-edge coloring of K_n there is some 1≤j≤k such that the graph formed by the edges colored j has a degree-monotone path of order m. We prove several nontrivial upper and lower bounds for M_k(m).

Original language	English
Pages (from-to)	124-131
Number of pages	8
Journal	Discrete Mathematics
Volume	340
Issue number	2
DOIs	https://doi.org/10.1016/j.disc.2016.07.025
State	Published - 6 Feb 2017

Bibliographical note

Publisher Copyright:
© 2016 Elsevier B.V.

Keywords

Degrees
Paths
Ramsey

ASJC Scopus subject areas

Theoretical Computer Science
Discrete Mathematics and Combinatorics

Access to Document

10.1016/j.disc.2016.07.025

Cite this

@article{fd3f04b5ad11478e99799bc8b2d9c60d,

title = "Ramsey numbers for degree monotone paths",

abstract = "A path v1,v2,…,vm in a graph G is degree-monotone if deg(v1)≤deg(v2)≤⋯≤deg(vm) where deg(vi) is the degree of vi in G. Longest degree-monotone paths have been studied in several recent papers. Here we consider the Ramsey type problem for degree monotone paths. Denote by Mk(m) the minimum number M such that for all n≥M, in any k-edge coloring of Kn there is some 1≤j≤k such that the graph formed by the edges colored j has a degree-monotone path of order m. We prove several nontrivial upper and lower bounds for Mk(m).",

keywords = "Degrees, Paths, Ramsey",

author = "Yair Caro and Raphael Yuster and Christina Zarb",

note = "Publisher Copyright: {\textcopyright} 2016 Elsevier B.V.",

year = "2017",

month = feb,

day = "6",

doi = "10.1016/j.disc.2016.07.025",

language = "English",

volume = "340",

pages = "124--131",

journal = "Discrete Mathematics",

issn = "0012-365X",

publisher = "Elsevier",

number = "2",

}

TY - JOUR

T1 - Ramsey numbers for degree monotone paths

AU - Caro, Yair

AU - Yuster, Raphael

AU - Zarb, Christina

PY - 2017/2/6

Y1 - 2017/2/6

N2 - A path v1,v2,…,vm in a graph G is degree-monotone if deg(v1)≤deg(v2)≤⋯≤deg(vm) where deg(vi) is the degree of vi in G. Longest degree-monotone paths have been studied in several recent papers. Here we consider the Ramsey type problem for degree monotone paths. Denote by Mk(m) the minimum number M such that for all n≥M, in any k-edge coloring of Kn there is some 1≤j≤k such that the graph formed by the edges colored j has a degree-monotone path of order m. We prove several nontrivial upper and lower bounds for Mk(m).

AB - A path v1,v2,…,vm in a graph G is degree-monotone if deg(v1)≤deg(v2)≤⋯≤deg(vm) where deg(vi) is the degree of vi in G. Longest degree-monotone paths have been studied in several recent papers. Here we consider the Ramsey type problem for degree monotone paths. Denote by Mk(m) the minimum number M such that for all n≥M, in any k-edge coloring of Kn there is some 1≤j≤k such that the graph formed by the edges colored j has a degree-monotone path of order m. We prove several nontrivial upper and lower bounds for Mk(m).

KW - Degrees

KW - Paths

KW - Ramsey

UR - http://www.scopus.com/inward/record.url?scp=84984830662&partnerID=8YFLogxK

U2 - 10.1016/j.disc.2016.07.025

DO - 10.1016/j.disc.2016.07.025

M3 - Article

AN - SCOPUS:84984830662

SN - 0012-365X

VL - 340

SP - 124

EP - 131

JO - Discrete Mathematics

JF - Discrete Mathematics

IS - 2

ER -

Ramsey numbers for degree monotone paths

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this