On the Restricted Size Ramsey Number

Denny Riama Silaban; Edy Tri Baskoro; Saladin Uttunggadewa

doi:10.1016/j.procs.2015.12.069

On the Restricted Size Ramsey Number

Denny Riama Silaban
, Edy Tri Baskoro
, Saladin Uttunggadewa

Department of Mathematics

Research output: Contribution to journal › Conference article › peer-review

7 Citations (Scopus)

Abstract

Let F, G, and H be simple graphs. We say F → (G, H) if for every 2-coloring of the edges of F there exists a monochromatic G or H in F. The Ramsey number r(G, H) is defined as min {|V (F)|: F → (G, H)}, while the restricted size Ramsey number r∗(G, H) is defined as min {|E (F)|: F → (G, H), |V (F) | = r(G, H)}. In this paper, we give lower and upper bounds for the restricted size Ramsey number for a path P3 versus cycles Cn.

Original language	English
Pages (from-to)	21-26
Number of pages	6
Journal	Procedia Computer Science
Volume	74
DOIs	https://doi.org/10.1016/j.procs.2015.12.069
Publication status	Published - 2015
Event	2nd International Conference of Graph Theory and Information Security, 2015 - Bandung, Indonesia Duration: 21 Sept 2015 → 23 Sept 2015

Keywords

Restricted size Ramsey number
cycle
path

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10.1016/j.procs.2015.12.069

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title = "On the Restricted Size Ramsey Number",

abstract = "Let F, G, and H be simple graphs. We say F → (G, H) if for every 2-coloring of the edges of F there exists a monochromatic G or H in F. The Ramsey number r(G, H) is defined as min \{|V (F)|: F → (G, H)\}, while the restricted size Ramsey number r∗(G, H) is defined as min \{|E (F)|: F → (G, H), |V (F) | = r(G, H)\}. In this paper, we give lower and upper bounds for the restricted size Ramsey number for a path P3 versus cycles Cn.",

keywords = "Restricted size Ramsey number, cycle, path",

author = "Silaban, \{Denny Riama\} and Baskoro, \{Edy Tri\} and Saladin Uttunggadewa",

note = "Funding Information: Acknowledgement. This research was supported by Research Grant ”Program Riset dan Inovasi KK-ITB” 2015, Ministry of Research, Technology, and Higher Education, Indonesia.; 2nd International Conference of Graph Theory and Information Security, 2015 ; Conference date: 21-09-2015 Through 23-09-2015",

year = "2015",

doi = "10.1016/j.procs.2015.12.069",

language = "English",

volume = "74",

pages = "21--26",

journal = "Procedia Computer Science",

issn = "1877-0509",

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TY - JOUR

T1 - On the Restricted Size Ramsey Number

AU - Silaban, Denny Riama

AU - Baskoro, Edy Tri

AU - Uttunggadewa, Saladin

N1 - Funding Information: Acknowledgement. This research was supported by Research Grant ”Program Riset dan Inovasi KK-ITB” 2015, Ministry of Research, Technology, and Higher Education, Indonesia.

PY - 2015

Y1 - 2015

N2 - Let F, G, and H be simple graphs. We say F → (G, H) if for every 2-coloring of the edges of F there exists a monochromatic G or H in F. The Ramsey number r(G, H) is defined as min {|V (F)|: F → (G, H)}, while the restricted size Ramsey number r∗(G, H) is defined as min {|E (F)|: F → (G, H), |V (F) | = r(G, H)}. In this paper, we give lower and upper bounds for the restricted size Ramsey number for a path P3 versus cycles Cn.

AB - Let F, G, and H be simple graphs. We say F → (G, H) if for every 2-coloring of the edges of F there exists a monochromatic G or H in F. The Ramsey number r(G, H) is defined as min {|V (F)|: F → (G, H)}, while the restricted size Ramsey number r∗(G, H) is defined as min {|E (F)|: F → (G, H), |V (F) | = r(G, H)}. In this paper, we give lower and upper bounds for the restricted size Ramsey number for a path P3 versus cycles Cn.

KW - Restricted size Ramsey number

KW - cycle

KW - path

UR - https://www.scopus.com/pages/publications/84964047289

U2 - 10.1016/j.procs.2015.12.069

DO - 10.1016/j.procs.2015.12.069

M3 - Conference article

AN - SCOPUS:84964047289

SN - 1877-0509

VL - 74

SP - 21

EP - 26

JO - Procedia Computer Science

JF - Procedia Computer Science

T2 - 2nd International Conference of Graph Theory and Information Security, 2015

Y2 - 21 September 2015 through 23 September 2015

ER -

On the Restricted Size Ramsey Number

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Keywords

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