Geodesic
Ramsey \((K_ {1,2},K_ 3)\)-minimal graphs
The electronic journal of combinatorics, Tome 12 (2005)
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For graphs $G,F$ and $H$ we write $G\rightarrow (F,H)$ to mean that if the edges of $G$ are coloured with two colours, say red and blue, then the red subgraph contains a copy of $F$ or the blue subgraph contains a copy of $H$. The graph $G$ is $(F,H)$-minimal (Ramsey-minimal) if $G\rightarrow (F,H)$ but $G'\not\rightarrow (F,H)$ for any proper subgraph $G'\subseteq G$. The class of all $(F,H)$-minimal graphs shall be denoted by $R (F,H)$. In this paper we will determine the graphs in $R(K_{1,2},K_3)$.
DOI : 10.37236/1917
Classification : 05C55
Mots-clés : generalised Ramsey number 
@article{10_37236_1917,
     author = {M. Borowiecki and I. Schiermeyer and E. Sidorowicz},
     title = {Ramsey {\((K_} {{1,2},K_} 3)\)-minimal graphs},
     journal = {The electronic journal of combinatorics},
     year = {2005},
     volume = {12},
     doi = {10.37236/1917},
     zbl = {1081.05071},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/1917/}
}
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M. Borowiecki; I. Schiermeyer; E. Sidorowicz. Ramsey \((K_ {1,2},K_ 3)\)-minimal graphs. The electronic journal of combinatorics, Tome 12 (2005). doi: 10.37236/1917

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