Proceedings - Mathematical Sciences

, Volume 127, Issue 5, pp 787–792 | Cite as

Connected size Ramsey number for matchings vs. small stars or cycles

  • Budi RahadjengEmail author
  • Edy Tri Baskoro
  • Hilda Assiyatun


The notation \(F\rightarrow (G,H)\) means that if the edges of F are colored red and blue, then the red subgraph contains a copy of G or the blue subgraph contains a copy of H. The connected size Ramsey number \(\hat{r}_c(G,H)\) of graphs G and H is the minimum size of a connected graph F satisfying \(F\rightarrow (G,H)\). For \(m \ge 2,\) the graph consisting of m independent edges is called a matching and is denoted by \(mK_2\). In 1981, Erdös and Faudree determined the size Ramsey numbers for the pair \((mK_2, K_{1,t})\). They showed that the disconnected graph \(mK_{1,t} \rightarrow (mK_2,K_{1,t})\) for \( t,m \ge 1\). In this paper, we will determine the connected size Ramsey number \(\hat{r}_c(nK_2, K_{1,3})\) for \(n\ge 2\) and \(\hat{r}_c(3K_2, C_4)\). We also derive an upper bound of the connected size Ramsey number \(\hat{r}_c(nK_2, C_4),\) for \(n\ge 4\).


Connected size Ramsey number cycle matching star 

2010 Mathematics Subject Classification

05D10 05C55 



This research was supported by Research Grant “Program Riset dan Inovasi KK-ITB”, Ministry of Research, Technology and Higher Education, Indonesia.


  1. 1.
    Erdös P and Faudree R J, Size Ramsey numbers involving matching, Colloquia Math. Societatis János Bolyai 37 (1981) 247–264MathSciNetGoogle Scholar
  2. 2.
    Erdös P, Faudree R J, Rousseau C C and Schelp R H, The size Ramsey number, Period. Math. Hungar. 9 (1978) 145–161MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    Faudree R J and Schelp R H, A survey of results on the size Ramsey number, Paul Erdös Math. II 10 (2002) 291–309MathSciNetzbMATHGoogle Scholar
  4. 4.
    Rahadjeng B, Baskoro E T and Assiyatun H, Connected size Ramsey numbers for matchings versus cycles or path, Proc. Comput. Sci. 74 (2015) 32–37CrossRefzbMATHGoogle Scholar
  5. 5.
    Rahadjeng B, Baskoro E T and Assiyatun H, Connected size Ramsey numbers of matchings and stars, AIP Conf. Proc. 1707 (2016) 020015, CrossRefGoogle Scholar

Copyright information

© Indian Academy of Sciences 2017

Authors and Affiliations

  1. 1.Combinatorial Mathematics Research Group, Faculty of Mathematics and Natural SciencesInstitut Teknologi Bandung (ITB)BandungIndonesia

Personalised recommendations