Geodesic
On path-quasar Ramsey numbers
Annales Universitatis Mariae Curie-Skłodowska. Mathematica , Tome 68 (2014) no. 2.

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Let G_1 and G_2 be two given graphs. The Ramsey number R(G_1,G_2) is the least integer r such that for every graph G on r vertices, either G contains a G_1 or G contains a G_2. Parsons gave a recursive formula to determine the values of R(P_n,K_1,m), where P_n is a path on n vertices and K_1,m is a star on m+1 vertices. In this note, we study the Ramsey numbers R(P_n,K_1∨ F_m), where F_m is a linear forest on m vertices. We determine the exact values of R(P_n,K_1∨ F_m) for the cases m≤ n and m≥ 2n, and for the case that F_m has no odd component. Moreover, we give a lower bound and an upper bound for the case n+1≤ m≤ 2n-1 and F_m has at least one odd component. 
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Li, Binlong; Ning, Bo. On path-quasar Ramsey numbers. Annales Universitatis Mariae Curie-Skłodowska. Mathematica , Tome 68 (2014) no. 2. http://geodesic.mathdoc.fr/item/AUM_2014_68_2_a3/

[1] Bondy, J. A., Murty, U. S. R., Graph Theory with Applications, American Elsevier Publishing Co., Inc., New York, 1976.

[2] Chen, Y., Zhang, Y., Zhang, K., The Ramsey numbers of paths versus wheels, Discrete Math. 290 (1) (2005), 85–87.

[3] Dirac, G. A., Some theorems on abstract graphs, Proc. London. Math. Soc. 2 (1952), 69–81.

[4] Faudree, R. J., Lawrence, S. L., Parsons, T. D., Schelp, R. H., Path-cycle Ramsey numbers, Discrete Math. 10 (2) (1974), 269–277.

[5] Graham, R. L., Rothschild, B. L., Spencer, J. H., Ramsey Theory, Second Edition, John Wiley Sons Inc., New York, 1990.

[6] Li, B., Ning, B., The Ramsey numbers of paths versus wheels: a complete solution, Electron. J. Combin. 21 (4) (2014), #P4.41.

[7] Parsons, T. D., Path-star Ramsey numbers, J. Combin. Theory, Ser. B 17 (1) (1974), 51–58.

[8] Rousseau, C. C., Sheehan, J., A class of Ramsey problems involving trees, J. London Math. Soc. 2 (3) (1978), 392–396.

[9] Salman, A. N. M., Broersma, H. J., Path-fan Ramsey numbers, Discrete Applied Math. 154 (9) (2006), 1429–1436.

[10] Salman, A. N. M., Broersma, H. J., Path-kipas Ramsey numbers, Discrete Applied Math. 155 (14) (2007), 1878–1884.

[11] Zhang, Y., On Ramsey numbers of short paths versus large wheels, Ars Combin. 89 (2008), 11–20.