Geodesic
Closing the gap on path-kipas Ramsey numbers
Binlong Li1 ; Yanbo Zhang2 ; Halina Bielak3 ; Hajo Broersma4 ; Premek Holub5
1Department of Mathematics, University of West Bohemia; European Centre of Excellence NTIS - New Technologies for the Information Society; P.O. Box 314, 306 14 Pilsen, Czech Republic; Department of Applied Mathematics, Northwestern Polytechnical University; Xi'an, Shaanxi 710072, P.R. China
2Faculty of Electrical Engineering, Mathematics and Computer Science, University of Twente, P.O.Box 217, 7500 AE Enschede, The Netherlands; Department of Mathematics, Nanjing University, Nanjing 210093, P.R. China
3Institute of Mathematics, Maria Curie-Sklodowska University; 20-031 Lublin, Poland
4Faculty of Electrical Engineering, Mathematics and Computer Science, University of Twente, P.O.Box 217, 7500 AE Enschede, The Netherlands
5University of West Bohemia Plzen Czech Republic
The electronic journal of combinatorics, Tome 22 (2015) no. 3
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Given two 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 $G_1$ is a subgraph of $G$, or $G_2$ is a subgraph of the complement of $G$. Let $P_n$ denote a path of order $n$ and $\widehat{K}_m$ a kipas of order $m+1$, i.e., the graph obtained from a $P_m$ by adding one new vertex $v$ and edges from $v$ to all vertices of the $P_m$.We close the gap in existing knowledge on exact values of the Ramsey numbers $R(P_n,\widehat{K}_m)$ by determining the exact values for the remaining open cases.
DOI : 10.37236/5007
Classification : 05C55, 05D10
Mots-clés : Ramsey number, path, kipas

Binlong Li  1   ; Yanbo Zhang  2   ; Halina Bielak  3   ; Hajo Broersma  4   ; Premek Holub  5

1 Department of Mathematics, University of West Bohemia; European Centre of Excellence NTIS - New Technologies for the Information Society; P.O. Box 314, 306 14 Pilsen, Czech Republic; Department of Applied Mathematics, Northwestern Polytechnical University; Xi'an, Shaanxi 710072, P.R. China
2 Faculty of Electrical Engineering, Mathematics and Computer Science, University of Twente, P.O.Box 217, 7500 AE Enschede, The Netherlands; Department of Mathematics, Nanjing University, Nanjing 210093, P.R. China
3 Institute of Mathematics, Maria Curie-Sklodowska University; 20-031 Lublin, Poland
4 Faculty of Electrical Engineering, Mathematics and Computer Science, University of Twente, P.O.Box 217, 7500 AE Enschede, The Netherlands
5 University of West Bohemia Plzen Czech Republic 
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     author = {Binlong Li and Yanbo Zhang and Halina Bielak and Hajo Broersma and Premek Holub},
     title = {Closing the gap on path-kipas {Ramsey} numbers},
     journal = {The electronic journal of combinatorics},
     year = {2015},
     volume = {22},
     number = {3},
     doi = {10.37236/5007},
     zbl = {1327.05229},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/5007/}
}
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Binlong Li; Yanbo Zhang; Halina Bielak; Hajo Broersma; Premek Holub. Closing the gap on path-kipas Ramsey numbers. The electronic journal of combinatorics, Tome 22 (2015) no. 3. doi: 10.37236/5007

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