Connected size Ramsey numbers of matchings and stars

Rahadjeng, Budi; Baskoro, Edy Tri; Assiyatun, Hilda

doi:10.1063/1.4940816

Cited by 6 publications

(4 citation statements)

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“…Some results on the connected size Ramsey number for a pairs of graphs were established. Rahadjeng et al [8] determined the connected size Ramsey number for the pairs (2K 2 , K 1,m ) and (3K 2 , K 1,m ). Then, in [7], they showed thatr c (nK 2 , K 1,3 ) = 4n − 1, for n ≥ 2.…”

Section: Introductionmentioning

confidence: 99%

The connected size Ramsey number for matchings versus small disconnected graphs

Assiyatun

Rahadjeng

Baskoro

2019

ejgta

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Let F, G, and H be simple graphs. The notation F → (G, H) means that if all the edges of F are arbitrarily colored by red or blue, then there always exists either a red subgraph G or a blue subgraph H. The size Ramsey number of graph G and H, denoted byr(G, H) is the smallest integer k such that there is a graph F with k edges satisfying F → (G, H). In this research, we will study a modified size Ramsey number, namely the connected size Ramsey number. In this case, we only consider connected graphs F satisfying the above properties. This connected size Ramsey number of G and H is denoted byr c (G, H). We will derive an upper bound ofr c (nK 2 , H), n ≥ 2 where H is 2P m or 2K 1,t , and find the exact values ofr c (nK 2 , H), for some fixed n.

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Section: Introductionmentioning

confidence: 99%

The connected size Ramsey number for matchings versus small disconnected graphs

Assiyatun

Rahadjeng

Baskoro

2019

ejgta

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“…On the other hand, if we view P 3 as K 1,2 , we may consider rc (nK 2 , K 1,m ). Assiyatun, Baskoro and Rahadjeng [14] proved that rc (nK 2 , K 1,m ) ≤ nm + n − 1. We conjecture that the upper bound matches the exact value as follows.…”

Section: Chapter III Conclusionmentioning

confidence: 99%

“…The size Ramsey numbers was modified by adding connectedness to F by Assiyatun, Baskoro and Rahadjeng [14]. They defined the connected size Ramsey number of G and H, denoted by rc (G, H), to be the smallest natural number k such that there exists a connected graph F with k edges and F → (G, H).…”

Section: Connected Size Ramsey Numbermentioning

confidence: 99%

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Connected size Ramsey numbers of matching and some graphs

Mungtumklang

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The connected size Ramsey number of graphs G and H, denoted by rc (G, H), is the smallest natural number k such that there exists a connected graph F with k edges and any red-blue edge-coloring of F contains a red copy of G or a blue copy of H.Assiyatun, Baskoro and Rahadjeng showed that rc (nK 2 , P 3 ) ≤ 5n−1 2 . Recently, Wang, Song, Zhang, and Zhang proved that rc (nK 2 , P 3 ) = 5n−1 2 . In this thesis, we give an alternative proof of this result.

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