Applications of Ramsey theory

Abstract This paper attempts to show that Ramsey theory really does have useful applications, by presenting four applications from the literature. The applications are from the fields of communications, information retrieval in computer science, and decisionmaking.

[1]  Andrew Chi-Chih Yao,et al.  Should Tables Be Sorted? , 1981, JACM.

[2]  Peter C. Fishburn,et al.  Partial orders of dimension 2 , 1972, Networks.

[3]  Ronald L. Graham,et al.  Rudiments of Ramsey theory , 1981 .

[4]  László Lovász,et al.  On the Shannon capacity of a graph , 1979, IEEE Trans. Inf. Theory.

[5]  Claude E. Shannon,et al.  The zero error capacity of a noisy channel , 1956, IRE Trans. Inf. Theory.

[6]  Ben Dushnik,et al.  Partially Ordered Sets , 1941 .

[7]  M. Rosenfeld ON A PROBLEM OF C. E. SHANNON IN GRAPH THEORY , 1967 .

[8]  P. Fishburn Intransitive indifference with unequal indifference intervals , 1970 .

[9]  Fred S. Roberts,et al.  What if utility functions do not exist? , 1972 .

[10]  Fred S. Roberts,et al.  Applied Combinatorics , 1984 .

[11]  V. Rosta On a ramsey-type problem of J. A. Bondy and P. Erdös. I , 1973 .

[12]  Peter C. Fishburn,et al.  PARTIAL ORDERS OF DIMENSION 2, INTERVAL ORDERS AND INTERVAL GRAPHS, , 1970 .

[13]  William T. Trotter,et al.  Characterization problems for graphs, partially ordered sets, lattices, and families of sets , 1976, Discret. Math..

[14]  Willem H. Haemers,et al.  On Some Problems of Lovász Concerning the Shannon Capacity of a Graph , 1979, IEEE Trans. Inf. Theory.

[15]  William T. Trotter,et al.  Dimension Theory for Ordered Sets , 1982 .

[16]  Alexander Schrijver,et al.  A comparison of the Delsarte and Lovász bounds , 1979, IEEE Trans. Inf. Theory.

[17]  Richard H. Schelp,et al.  All Ramsey numbers for cycles in graphs , 1974, Discret. Math..

[18]  Richard J. Lipton,et al.  Multi-party protocols , 1983, STOC.

[19]  Ronald L. Graham,et al.  On Multicolor Ramsey Numbers for Complete Bipartite Graphs , 1975 .

[20]  E. Szpilrajn Sur l'extension de l'ordre partiel , 1930 .

[21]  William T. Trotter,et al.  A Bound on the Dimension of Interval Orders , 1976, J. Comb. Theory, Ser. A.