On Size Bipartite and Tripartite Ramsey Numbers for  The Star Forest and Path on 3 Vertices

Lusiani, Anie; Baskoro, Edy Tri; Saputro, Suhadi Wido

doi:10.5614/j.math.fund.sci.2020.52.1.1

Cited by 3 publications

(2 citation statements)

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“…The size multipartite Ramsey numbers of small stars versus the union of stars have been studied. In [8], Lusiani et al determined the size multipartite Ramsey numbers m j (G, K 1,2 ), for j = 2, 3, where G is a union of two, three, or four distinct stars. In [6,7], Lusiani et al determined the size multipartite Ramsey numbers m j (mK 1,n , H) where H = K 1,2 or H = K 1,3 .…”

Section: Introductionmentioning

confidence: 99%

Multipartite Ramsey Numbers of Union of Stars

Anuwiksa

Simanjuntak

Baskoro

2022

EJGTA

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Let s and k be positive integers with k ≥ 2 and G 1 , G 2 , . . . , G k be simple graphs. The set multipartite Ramsey number, denoted by M s (G 1 , G 2 , . . . , G k ), is the smallest positive integer c such that any k-coloring of the edges of K c×s contains a monochromatic copy of G i in color i for some i ∈ {1, 2, . . . , k}. The size multipartite Ramsey number, denoted by m c (G 1 , G 2 , . . . , G k ), is the smallest positive integer s such that any k-coloring of the edges of K c×s contains a monochromatic copy of G i in color i for some i ∈ {1, 2, . . . , k}. In this paper, we establish some lower and upper bounds, and some exact values of multipartite Ramsey numbers for the union of stars.

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Section: Introductionmentioning

confidence: 99%

Multipartite Ramsey Numbers of Union of Stars

Anuwiksa

Simanjuntak

Baskoro

2022

EJGTA

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“…Syafrizal et al determined the size multipartite Ramsey numbers of path versus path [16]. m 3 (G, P 3 ) and m 2 (G, P 3 ) where G is a star forest, namely a disjoint union of heterogeneous stars have been studied in [17]. The exact values of the size Ramsey numbers m j (P 3 , K 2,n ) and m j (P 4 , K 2,n ) for j ≥ 3 computed in [18].…”

Section: Introductionmentioning

confidence: 99%

The Size, Multipartite Ramsey Numbers for nK2 Versus Path–Path and Cycle

2021

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For given graphs G1,G2,…,Gn and any integer j, the size of the multipartite Ramsey number mj(G1,G2,…,Gn) is the smallest positive integer t such that any n-coloring of the edges of Kj×t contains a monochromatic copy of Gi in color i for some i, 1≤i≤n, where Kj×t denotes the complete multipartite graph having j classes with t vertices per each class. In this paper, we computed the size of the multipartite Ramsey numbers mj(K1,2,P4,nK2) for any j,n≥2 and mj(nK2,C7), for any j≤4 and n≥2.

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