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All Journal Epsilon: Jurnal Matematika Murni dan Terapan Electronic Journal of Graph Theory and Applications (EJGTA) Journal of Mathematical and Fundamental Sciences Kubik NUMERICAL (Jurnal Matematika dan Pendidikan Matematika) JURNAL PENGABDIAN KEPADA MASYARAKAT Indonesian Journal of Combinatorics Jurnal ABDINUS : Jurnal Pengabdian Nusantara Jurnal Lebesgue : Jurnal Ilmiah Pendidikan Matematika, Matematika dan Statistika KUBIK: Jurnal Publikasi Ilmiah Matematika ARSY : Jurnal Aplikasi Riset kepada Masyarakat Industrial Research Workshop and National Seminar International Journal of Trends in Mathematics Education Research (IJTMER) KOPEMAS
Lusiani, Anie
Combinatorial Mathematics Research Group Faculty Of Mathematics And Natural Sciences, Institut Teknologi Bandung Jalan Ganesa 10 Bandung, Indonesia
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Journal : Indonesian Journal of Combinatorics

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On size multipartite Ramsey numbers for stars Anie Lusiani; Edy Tri Baskoro; Suhadi Wido Saputro
Indonesian Journal of Combinatorics Vol 3, No 2 (2019)
Publisher : Indonesian Combinatorial Society (InaCombS)

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (322.917 KB) | DOI: 10.19184/ijc.2019.3.2.4

Abstract

Burger and Vuuren defined the size multipartite Ramsey number for a pair of complete, balanced, multipartite graphs mj(Kaxb,Kcxd), for natural numbers a,b,c,d and j, where a,c >= 2, in 2004. They have also determined the necessary and sufficient conditions for the existence of size multipartite Ramsey numbers mj(Kaxb,Kcxd). Syafrizal et al. generalized this definition by removing the completeness requirement. For simple graphs G and H, they defined the size multipartite Ramsey number mj(G,H) as the smallest natural number t such that any red-blue coloring on the edges of Kjxt contains a red G or a blue H as a subgraph. In this paper, we determine the necessary and sufficient conditions for the existence of multipartite Ramsey numbers mj(G,H), where both G and H are non complete graphs. Furthermore, we determine the exact values of the size multipartite Ramsey numbers mj(K1,m, K1,n) for all integers m,n >= 1 and j = 2,3, where K1,m is a star of order m+1. In addition, we also determine the lower bound of m3(kK1,m, C3), where kK1,m is a disjoint union of k copies of a star K1,m and C3 is a cycle of order 3.
Co-Authors Agus Binarto Agus Binarto Agus Binarto Anny Suryani Anny Suryani Binarto, Agus Edy Tri Baskoro Endang Habinuddin Euis Sartika Habinuddin, Endang Hadiani, Fatmi Hadiningrum, Kunlestiowati hazma hazma Hedi Hedi, Hedi Irfani Azis Muldiani, Ratu Fenny Nani Yuningsih Nuryati, Neneng Sardjito Sardjito Sartika, Euis Siti Samsiyah Purwaningsih Siti Syamsiah Purwaningsih Suhadi Wido Saputro Suhadi Wido Saputro Suhadi Wido Saputro Suhartini, Ida Wastu Kurning Purbandini Yuliah, Siti