Critical Graphs for R(P_n, P_m) and the Star-Critical Ramsey Number for Paths

• Autorzy: Jonelle Hook
• Języki publikacji: EN

Abstrakty

EN

The graph Ramsey number R(G,H) is the smallest integer r such that every 2-coloring of the edges of Kr contains either a red copy of G or a blue copy of H. The star-critical Ramsey number r∗(G,H) is the smallest integer k such that every 2-coloring of the edges of Kr − K1,r−1−k contains either a red copy of G or a blue copy of H. We will classify the critical graphs, 2-colorings of the complete graph on R(G,H) − 1 vertices with no red G or blue H, for the path-path Ramsey number. This classification will be used in the proof of r∗(Pn, Pm).

Słowa kluczowe

EN

Ramsey number; critical graph; star-critical Ramsey number; path

• Wydawca: De Gruyter Open
• Czasopismo: Discussiones Mathematicae Graph Theory
• Rocznik: 2015
• Tom: 35
• Numer: 4
• Strony: 689-701

Daty

wydano

2015-11-01

otrzymano

2014-10-20

poprawiono

2015-02-18

zaakceptowano

2015-02-18

online

2015-11-10

Twórcy

autor

Jonelle Hook

• Mount St. Mary’s University Department of Mathematics and Computer Science Emmitsburg, MD 21727

Bibliografia

• [1] L. Gerencsér and A. Gyárfás, On Ramsey-type problems, Ann. Univ. Sci. Budapest. Eötvös Sect. Math. 10 (1967) 167-170.
• [2] J. Hook, The classification of critical graphs and star-critical Ramsey numbers (Ph.D. Thesis, Lehigh University, 2010).
• [3] J. Hook and G. Isaak, Star-critical Ramsey numbers, Discrete Appl. Math. 159 (2011) 328-334. doi:10.1016/j.dam.2010.11.007[Crossref]
• [4] R.J. Faudree, S.L. Lawrence, T.D. Parsons and R.H. Schelp, Path-cycle Ramsey numbers, Discrete Math. 10 (1974) 269-277. doi:10.1016/0012-365X(74)90122-8
• [5] R.J. Faudree and R.H. Schelp, All Ramsey numbers for cycles in graphs, Discrete Math. 8 (1974) 313-329. doi:10.1016/0012-365X(74)90151-4
• [6] D.B. West, Introduction to Graph Theory (Second Ed., Prentice Hall, Upper Saddle River, New Jersey, 2000).

Identyfikatory

DOI

10.7151/dmgt.1827