On The Restricted Size Ramsey Number

Silaban, Denny Riama; Baskoro, Edy Tri; Uttunggadewa, Saladin

doi:10.1016/j.procs.2015.12.069

Cited by 4 publications

(8 citation statements)

References 5 publications

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“…The size Ramsey number for a pair of graphs was introduced by Erdős et al in 1978 [4], while the restricted size Ramsey number for a pair of graphs is a direct consequence of the concept of Ramsey and size Ramsey number in graphs. Some previous results on the (restricted) size Ramsey number of graphs was given in [1,5] and the previous results on the restricted size Ramsey number involving a P 3 can be found in [9,10,11,12,13].…”

Section: Introductionmentioning

confidence: 94%

On the restricted size Ramsey number for P3 versus dense connected graphs

Silaban

Baskoro

Uttunggadewa

2020

EJGTA

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Let F , G and H be simple graphs. A graph F is said a (G, H) arrowing graph if in any red-blue coloring of edges of F we can find a red G or a blue H. The size Ramsey number of G and H, r(G, H), is the minimum size of F. If the order of F equals to the Ramsey number of G and H, r(G, H), then the minimum size of F is called the restricted size Ramsey number of G and H, r ⇤ (G, H). The Ramsey number of G and H, r(G, H), is the minimum order of F. In this paper, we study the restricted size number involving a P 3. The value of r ⇤ (P 3 , K n) has been given by Faudree and Sheehan. Here, we examine r ⇤ (P 3 , H) where H is dense connected graph.

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Section: Introductionmentioning

confidence: 94%

On the restricted size Ramsey number for P3 versus dense connected graphs

Silaban

Baskoro

Uttunggadewa

2020

EJGTA

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“…In [9] Silaban et al proved that r * (P 3 , C n ) ≤ 2n − 1. In this section we will show that this upper bound can be improved and we prove the following theorem.…”

Section: Upper Bounds For R * (P 3 C N )mentioning

confidence: 99%

“…). For all integers n ≥ 4, In 2015, Silaban et al [9] proved the lower and the upper bound for the restricted size Ramsey number for P 3 and cycles. At the end of our article we improve the upper bound for this number.…”

Section: Theorem 2 ([5]mentioning

confidence: 99%

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Restricted size Ramsey number for P3 versus cycle

Cyman

Dzido

2020

EJGTA

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Let F , G and H be simple graphs. We say F → (G, H) if for every red-blue coloring of the edges of F there exists a red copy of G or a blue copy of H in F. The Ramsey number r(G, H) is defined as r(G, H) = min{|V (F)| : F → (G, H)}, while the restricted size Ramsey number r * (G, H) is defined as r * (G, H) = min{|E(F)| : F → (G, H), |V (F)| = r(G, H)}. In this paper we determine previously unknown restricted size Ramsey numbers r * (P 3 , C n) for 7 ≤ n ≤ 12. We also give new upper bound r * (P 3 , C n) ≤ 2n − 2 for even n ≥ 10.

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“…It had shown that r * (P 3 , C 3 ) = 8, r * (P 3 , C 4 ) = 6, r * (P 3 , C 5 ) = 9. In 2015 Silaban et al proved the last known exact value, namely r * (P 3 , C 6 ) = 9 [8]. In addition, they give lower and upper bound for r * (P 3 , C n ), where n ≥ 8 is even (see below Theorem 3).…”

Section: Introductionmentioning

confidence: 99%

Restricted size Ramsey number for $P_3$ versus cycles

Cyman,

Dzido

2017

Preprint

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On The Restricted Size Ramsey Number

Cited by 4 publications

References 5 publications

On the restricted size Ramsey number for P3 versus dense connected graphs

On the restricted size Ramsey number for P3 versus dense connected graphs

Restricted size Ramsey number for P3 versus cycle

Restricted size Ramsey number for $P_3$ versus cycles

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