On Size Multipartite Ramsey Numbers for Stars versus Cycles

Lusiani, Anie; Sy, Syafrizal; Baskoro, Edy Tri; Jayawardene, Chula J.

doi:10.1016/j.procs.2015.12.070

Cited by 8 publications

(7 citation statements)

References 4 publications

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“…Recently, Lusiani et al [6] showed the size multipartite Ramsey numbers for stars versus cycles. Now, we investigate the size bipartite Ramsey numbers for stars versus cycles.…”

Section: Stars Versus Cyclesmentioning

confidence: 99%

On size multipartite Ramsey numbers for stars versus paths and cycles

Lusiani

Baskoro

Saputro

2017

ejgta

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Let K l×t be a complete, balanced, multipartite graph consisting of l partite sets and t vertices in each partite set. For given two graphs G 1 and G 2 , and integer j ≥ 2, the size multipartite Ramsey number m j (G 1 , G 2 ) is the smallest integer t such that every factorization of the graph K j×t := F 1 ⊕ F 2 satisfies the following condition: either F 1 contains G 1 or F 2 contains G 2 . In 2007, Syafrizal et al. determined the size multipartite Ramsey numbers of paths P n versus stars, for n = 2, 3 only. Furthermore, Surahmat et al. (2014) gave the size tripartite Ramsey numbers of paths P n versus stars, for n = 3, 4, 5, 6. In this paper, we investigate the size tripartite Ramsey numbers of paths P n versus stars, with all n ≥ 2. Our results complete the previous results given by Syafrizal et al. and Surahmat et al. We also determine the size bipartite Ramsey numbers m 2 (K 1,m , C n ) of stars versus cycles, for n ≥ 3, m ≥ 2.

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“…Recently, Lusiani et al [6] showed the size multipartite Ramsey numbers for stars versus cycles. Now, we investigate the size bipartite Ramsey numbers for stars versus cycles.…”

Section: Stars Versus Cyclesmentioning

confidence: 99%

On size multipartite Ramsey numbers for stars versus paths and cycles

Lusiani

Baskoro

Saputro

2017

ejgta

Self Cite

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“…Burgeet et al have done a research on the value of

, under the condition which G and H are both complete multipartite graphs in [6] . Recently, the exact value of

was calculated for certain graph classes, see [7] , [8] , [9] alongside related references, which normally can be boosted to various colors, see [10] , [11] , [12] , [13] , [14] , [15] , [16] , [17] . The multipartite Ramsey number

in case that G is considered as a path or a cycle including n vertices and

23

, has been studied in [14] .…”

Section: Introductionmentioning

confidence: 99%

Some results on the multipartite Ramsey numbers m(C3,C,n1K2,n2K2,…,nK2)

Rowshan

Gholami

Shateyi

2022

Heliyon

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“…Recently the M-R-number m j (G 1 , G 2 ) have been study for special classes, see [2,3,7,10] and its references. Which can be naturally extended to several colors, see [5,6,8,9,11,[13][14][15]. In [8], Lusiani et al determined the M-R-number m j (K 1,m , G), for j = 2, 3 where G is a P n or a C n .…”

Section: Introductionmentioning

confidence: 99%

The Multipartite Ramsey numbers $m_j(nK_2,C_7)$

Rowshan¹

2021

Preprint

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Assume that Kj×n be a complete, multipartite graph consisting of j partite sets and n vertices in each partite set. For given graphs G1 and G2, the multipartite Ramsey number (M-R-number) mj(G1, G2) is the smallest integer t such that any subgraph G of the Kj×t, either G contains a copy of G1 or its complement relative to Kj×t contains a copy of G2. C. J. Jayawardene, E. T. Baskoro et al. (2016) gave the size of M-R-numbe mj(nK2, C7) for j ≥ 2 and n ≤ 6. Y. gave the size of M-R-number mj(nK2, C7) for j = 2, 3, 4 and n ≥ 2. In this article we compute the size of M-R-number mj(nK2, C7), for each j ≥ 5 and n ≥ 2.

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On Size Multipartite Ramsey Numbers for Stars versus Cycles

Cited by 8 publications

References 4 publications

On size multipartite Ramsey numbers for stars versus paths and cycles

On size multipartite Ramsey numbers for stars versus paths and cycles

Some results on the multipartite Ramsey numbers m(C3,C,n1K2,n2K2,…,nK2)

The Multipartite Ramsey numbers $m_j(nK_2,C_7)$

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