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Discussiones Mathematicae Graph Theory 30(4) (2010) 637-649
DOI: https://doi.org/10.7151/dmgt.1519

ON RAMSEY (K_1,2, C₄)-MINIMAL GRAPHS

Tomás Vetrí k School of Mathematical Sciences University of KwaZulu-Natal Durban, South Africa e-mail: tomas.vetrik@gmail.com

Lyra Yulianti  and  Edy Tri Baskoro Combinatorial Mathematics Research Division Faculty of Mathematics and Natural Sciences Institut Teknologi Bandung Bandung, Indonesia e-mail: lyra@students.itb.ac.id e-mail: ebaskoro@math.itb.ac.id

Abstract

For graphs F, G and H, we write F → (G,H) to mean that any red-blue coloring of the edges of F contains a red copy of G or a blue copy of H. The graph F is Ramsey (G,H)-minimal if F →(G,H) but F^* -/→ (G, H) for any proper subgraph F^* ⊂ F. We present an infinite family of Ramsey (K_1,2,C₄)-minimal graphs of any diameter ≥ 4.

Keywords: Ramsey-minimal graph, edge coloring, diameter of a graph.

2010 Mathematics Subject Classification: 05C55, 05D10.

References

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Received 3 March 2009
Revised 13 January 2010
Accepted 13 January 2010