The Ramsey numbers for some subgraphs of generalized wheels versus cycles and paths
Halina Bielak ; Kinga Dąbrowska
Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica, Tome 69 (2015), / Harvested from The Polish Digital Mathematics Library
Access to full text
Full (PDF)

The Ramsey number R(G,H) for a pair of graphs G and H is defined as the smallest integer n such that, for any graph F on n vertices, either F contains G or F¯ contains H as a subgraph, where F¯ denotes the complement of F. We study Ramsey numbers for some subgraphs of generalized wheels versus cycles and paths and determine these numbers for some cases. We extend many known results studied in [5, 14, 18, 19, 20]. In particular we count the numbers R(K1+Ln,Pm) and R(K1+Ln,Cm) for some integers m, n, where Ln is a linear forest of order n with at least one edge.

Publié le : 2015-01-01
EUDML-ID : urn:eudml:doc:289826 
@article{bwmeta1.element.ojs-doi-10_17951_a_2015_69_2_1-7,
     author = {Halina Bielak and Kinga D\k abrowska},
     title = {The Ramsey numbers for some subgraphs of generalized wheels versus cycles and paths},
     journal = {Annales Universitatis Mariae Curie-Sk\l odowska, sectio A -- Mathematica},
     volume = {69},
     year = {2015},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.ojs-doi-10_17951_a_2015_69_2_1-7}
}

Halina Bielak; Kinga Dąbrowska. The Ramsey numbers for some subgraphs of generalized wheels versus cycles and paths. Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica, Tome 69 (2015) . http://gdmltest.u-ga.fr/item/bwmeta1.element.ojs-doi-10_17951_a_2015_69_2_1-7/

Burr, S. A., Ramsey numbers involving graphs with long suspended paths,

J. London Math. Soc. 24 (2) (1981), 405-413.

Burr, S. A., Erdos, P., Generalization of a Ramsey-theoretic result of Chvatal, J. Graph Theory 7 (1983), 39-51.

Chen, Y., Cheng, T. C. E., Ng, C. T., Zhang, Y., A theorem on cycle-wheel Ramsey number, Discrete Math. 312 (2012), 1059-1061.

Chen, Y., Cheng, T. C. E., Miao, Z., Ng, C. T., The Ramsey numbers for cycles versus wheels of odd order, Appl. Math. Letters 22 (2009), 875-1876.

Chen, Y., Zhang, Y., Zhang, K., The Ramsey numbers of paths versus wheels, Discrete Math. 290 (2005), 85-87.

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

Faudree, R. J., Schelp, R. H., All Ramsey numbers for cycles in graphs, Discrete Math. 8 (1974), 313-329.

Karolyi, G., Rosta, V., Generalized and geometric Ramsey numbers for cycles, Theoretical Computer Science 263 (2001), 87-98.

Lin, Q., Li, Y., Dong, L., Ramsey goodness and generalized stars, Europ. J. Combin. 31 (2010), 1228-1234.

Radziszowski, S. P., Small Ramsey numbers, The Electronic Journal of Combinatorics (2014), DS1.14.

Radziszowski, S. P., Xia, J., Paths, cycles and wheels without antitriangles,

Australasian J. Combin. 9 (1994), 221-232.

Rosta, V.,On a Ramsey type problem of J. A. Bondy and P. Erdos, I, II, J. Combin. Theory Ser. B 15 (1973), 94-120.

Salman, A. N. M., Broersma, H. J., On Ramsey numbers for paths versus wheels, Discrete Math. 307 (2007), 975-982.

Shi, L., Ramsey numbers of long cycles versus books or wheels, European J. Combin. 31 (2010), 828-838.

Surahmat, Baskoro, E. T., Broersma, H. J., The Ramsey numbers of large cycles versus small wheels, Integers 4 (2004), A10.

Surahmat, Baskoro, E. T., Tomescu, I., The Ramsey numbers of large cycles versus odd wheels, Graphs Combin. 24 (2008), 53-58.

Surahmat, Baskoro, E. T., Tomescu, I., The Ramsey numbers of large cycles versus wheels, Discrete Math. 306 (24) (2006), 3334-3337.

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

Zhang, L., Chen, Y., Cheng, T. C., The Ramsey numbers for cycles versus wheels of even order, European J. Combin. 31 (2010), 254-259.

Zhang, Y., Chen, Y., The Ramsey numbers of wheels versus odd cycles, Discrete Math. 323 (2014), 76-80.