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Connected Size Ramsey Numbers for The Pair Complete Graph of Order Two versus Union Complete Graph of Order Three

Jurnal Matematika, Statistika dan Komputasi · Vol. 21 No. 2 (2025) · pp. 601–607

DOI
10.20956/j.v21i2.41850
ISSN
2614-8811, 1858-1382
Published
2025-01-12
Publisher
Department of Mathematics, Hasanuddin University
Language
en
License
creativecommons.org/licenses/by/4.0

Abstract

Let F,G, and H be finite, simple, and undirected graphs. The connected size Ramsey number r ̂_c (G,H) of graph G and H is the least integer k such that there is a connected graph F with k edges and if the edge set of F is arbitrarily colored by red or blue, then there always exists either a red copy of G or a blue copy of H. This paper shows that the connected size Ramsey number r ̂_c (2K_2,〖nK〗_3 )=4n+3, for n≥4.

Keywords

Collaboration network of the authors

30 authors · 75 co-authorship links · 3 across different organisations

Hover or tap a name to highlight its co-authors. Double-click to open the author's page.

  • Universitas Halu Oleo
  • Telkom University
  • Affiliation unknown
  • Different organisations
  • Same organisation
  • Affiliation unknown
  • Thicker line = more joint articles · bigger circle = more articles
Show as table
Co-authorOrganisationJoint articles
Loeky HaryantoAffiliation unknown2
Budi NurwahyuAffiliation unknown2
Ahmad Syukur DamingAffiliation unknown2
Amir Kamal AmirAffiliation unknown2
Ari Moesriami BarmawiTelkom University1
Rimba HamidUniversitas Halu Oleo1
Nana SumarnaUniversitas Halu Oleo1
La Ili La IliAffiliation unknown1
Aris BadaraUniversitas Halu Oleo1
Amirudin RahimAffiliation unknown1
Ida SriwatyAffiliation unknown1
Waode SuarniAffiliation unknown1
Saleh SalehAffiliation unknown1
La Ndia La NdiaAffiliation unknown1
Andi SadapottoAffiliation unknown1
Haidir JibranAffiliation unknown1
Irfan Hakim MaridiAffiliation unknown1
Amanda Putri sAffiliation unknown1
Dhea Rizky MalindaAffiliation unknown1
Denaya Mutiara SalsaAffiliation unknown1
Dila Amelia PutriAffiliation unknown1
Vanessa J.A. PandelakiAffiliation unknown1
Safriadi SafriadiAffiliation unknown1
St. Munieroh FachrunnisaAffiliation unknown1
Naimah ArisAffiliation unknown1
Haspika HaspikaAffiliation unknown1
Muh NurAffiliation unknown1
Ananda Dwi Nabila NandaAffiliation unknown1

Affiliations come from OpenAlex; journal OAI-PMH metadata carries none. Authors without an OpenAlex ID are matched by name, which can merge or split people.

Metadata source: OAI-PMH (metadata jurnal) https://journal.unhas.ac.id/index.php/jmsk/oai, first harvested 5 Nov 2026, last seen 5 Nov 2026.
Original metadata (oai_dc) 
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	<dc:title xml:lang="en">Connected Size Ramsey Numbers for The Pair Complete Graph of Order Two versus Union Complete Graph of Order Three </dc:title>
	<dc:creator xml:lang="en">Hasmawati, Hasmawati</dc:creator>
	<dc:creator xml:lang="en">Indrayani, Sri</dc:creator>
	<dc:subject xml:lang="en">graph; connected; size Ramsey number; complete graph.</dc:subject>
	<dc:subject xml:lang="en">connected</dc:subject>
	<dc:subject xml:lang="en">size Ramsey number</dc:subject>
	<dc:subject xml:lang="en">complete graph</dc:subject>
	<dc:description xml:lang="en">Let F,G, and H be finite, simple, and undirected graphs. The connected size Ramsey number r ̂_c (G,H) of graph G and  H is the least integer k such that there is a connected graph F with k edges and if the edge set of F is arbitrarily colored by red or blue, then there always exists either a red copy of G or a blue copy of  H. This paper shows that the connected size Ramsey number r ̂_c (2K_2,〖nK〗_3 )=4n+3,  for n≥4.</dc:description>
	<dc:publisher xml:lang="en">Department of Mathematics, Hasanuddin University</dc:publisher>
	<dc:date>2025-01-12</dc:date>
	<dc:type>info:eu-repo/semantics/article</dc:type>
	<dc:type>info:eu-repo/semantics/publishedVersion</dc:type>
	<dc:format>application/pdf</dc:format>
	<dc:identifier>https://journal.unhas.ac.id/index.php/jmsk/article/view/41850</dc:identifier>
	<dc:identifier>10.20956/j.v21i2.41850</dc:identifier>
	<dc:source xml:lang="en">Jurnal Matematika, Statistika dan Komputasi; Vol. 21 No. 2 (2025): JANUARY 2025; 601-607</dc:source>
	<dc:source>2614-8811</dc:source>
	<dc:source>1858-1382</dc:source>
	<dc:language>en</dc:language>
	<dc:relation>https://journal.unhas.ac.id/index.php/jmsk/article/view/41850/12455</dc:relation>
	<dc:rights xml:lang="en">Copyright (c) 2025 Jurnal Matematika, Statistika dan Komputasi</dc:rights>
	<dc:rights xml:lang="en">https://creativecommons.org/licenses/by/4.0</dc:rights>
</oai_dc:dc>