Geodesic
On multicolor Ramsey number of paths versus cycles
The electronic journal of combinatorics, Tome 18 (2011) no. 1
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Let $G_1, G_2, G_3, \ldots , G_t$ be graphs. The multicolor Ramsey number $R(G_1, G_2, \ldots, G_t)$ is the smallest positive integer $n$ such that if the edges of a complete graph $K_n$ are partitioned into $t$ disjoint color classes giving $t$ graphs $H_1,H_2,\ldots,H_t$, then at least one $H_i$ has a subgraph isomorphic to $G_i$. In this paper, we provide the exact value of $R(P_{n_1}, P_{n_2},\ldots, P_{n_t},C_k)$ for certain values of $n_i$ and $k$. In addition, the exact values of $R(P_5,C_4,P_k)$, $R(P_4,C_4,P_k)$, $R(P_5,P_5,P_k)$ and $R(P_5,P_6,P_k)$ are given. Finally, we give a lower bound for $R(P_{2n_1}, P_{2n_2},\ldots, P_{2n_t})$ and we conjecture that this lower bound is the exact value of this number. Moreover, some evidence is given for this conjecture.
DOI : 10.37236/511
Classification : 05C15, 05C55, 05C35
Mots-clés : Ramsey nubmer, paths, cycles 
@article{10_37236_511,
     author = {Gholam Reza Omidi and Ghaffar Raeisi},
     title = {On multicolor {Ramsey} number of paths versus cycles},
     journal = {The electronic journal of combinatorics},
     year = {2011},
     volume = {18},
     number = {1},
     doi = {10.37236/511},
     zbl = {1217.05093},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/511/}
}
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Gholam Reza Omidi; Ghaffar Raeisi. On multicolor Ramsey number of paths versus cycles. The electronic journal of combinatorics, Tome 18 (2011) no. 1. doi: 10.37236/511

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