Geodesic
The Ramsey number
The electronic journal of combinatorics, Tome 18 (2011) no. 1
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For two given graphs $G_1$ and $G_2$, the Ramsey number $r(G_1,G_2)$ is the smallest integer $n$ such that for any graph $G$ of order $n$, either $G$ contains $G_1$ or the complement of $G$ contains $G_2$. Let $K_m$ denote a complete graph of order $m$ and $K_n-P_3$ a complete graph of order $n$ without two incident edges. In this paper, we prove that $r(K_5-P_3,K_5)=25$ without help of computer algorithms.
DOI : 10.37236/577
Classification : 05C55 
@article{10_37236_577,
     author = {Luis Boza},
     title = {The {Ramsey} number},
     journal = {The electronic journal of combinatorics},
     year = {2011},
     volume = {18},
     number = {1},
     doi = {10.37236/577},
     zbl = {1217.05160},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/577/}
}
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Luis Boza. The Ramsey number. The electronic journal of combinatorics, Tome 18 (2011) no. 1. doi: 10.37236/577

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