PART I: INF & FIN RAMSEY: Graphs & Hypergraphs

Jan 28 Intro to the Course

Jan 28 Infinite Ramsey Thm For Graphs

Infinite Ram to Finite Ram For Graphs

Finite Ram Thm For Graphs,NOTES

Infinite Ramsey Thm For 3-Hypergraphs

Finite Ramsey Thm For 3-Hypergraphs-TOW bounds

ADAM AND ISSAC HAVE ALREADY READ THE ABOVE.

Prim Rec functions

Goodstein Sequences

ADAM AND ISSAC AND JAMES, STOP HERE.

Well Quasi Orderings,NOTES,Kruskal Tree Thm,PAPER. OPT

Better Bounds in 3-hyper Ramsey,3hramsey

APP: Thin Set Thm

APP: Logic, NOTES

Prim Rec functions

Goodstein Sequences

Better Bounds in 3-hyper Ramsey,3hramsey

APP: Data St,PAPER NOTES: one probe

APP: Convex Sets,SURVEY. OPT,Adv PAPER, WEBSITE of Papers, Exposition of Orig Paper

Notes on Computable Ramsey. OPT,Paper on Comp Ramsey. OPT,Survey of CompComb. OPT

Large Ramsey Thm, NOTES, NOTES on LR for Ordinals. OPT

PH Numbers. OPT,PAPER on PH Nums. OPT

Inf Can Ram,Inf Can Ram NOTES,Finite CR NOTES

Mileti's proof of Can Ram,NOTES

a-ary Can Ram. OPT

APP: Distances and Areas. OPT (may shorten)

NOTES: The Can Large Ram Thm. OPT

PART II: MORE FINITE RAMSEY THEORY

Small Ram Num,PAPER on R(3,6). OPT

Slightly Better Upper Bounds on R(k)

Two Triangles and Ramsey Multiplicity

Lower Bounds on Ram Numbs

About Lower Bounds on Ram Numbers, PAPER with better LB. OPT

Prob Method: Turan's Theorem

Prob Method: Dom Sets

Prob Method: Sum Free Sets, OPT

Prob Method: Distinct Diffs. OPT

PART III: GRAPH RAMSEY THEORY

Graham's GRT

Irving's GRT

Spencer's GRT

Prob Meth for LB on Ram Numbs,

PAPER with better LB

Prob Method: Turan's Thm (last part)

Adv PAPER, WEBSITE of Papers, Exposition of Orig Paper

PART IV: VDW's THM

Grid Coloring

Coloring the 15 x 15 grid

Dom Set HW Sol,

Sq Theorem

VDW

Are There Better Bounds on the VDW Numbers?

W(3,k),PAPER

Poly VDW,BOOK with pvdw,PAPER with pvdw

Extended VDW Theorem

APP Consecutive Sqs. OPT

APP: Graphs with large girth and Chrom Num. OPT

minicoures on Finite Geom and Ramsey, OPT

Rado's thm,Distinct Rado,Distinct Rado NOTES,Pythagoean Ramsey

Folkman's thm

APP: Schur + FLT(4) imply primes infinite,PAPER

APP: Multi Party Comm Comp,PAPER, OPT,PAPER, OPT

APP: Hilbert's Irred Thm

GKKZP polyvdw paper

PART V: EUCLIDEIAN RAMSEY THEORY

Intro to ERT and Chrom Numb of Plane

C4 Ramsey (needed for Unit Sq),Alt Proof. OPT

Unit Sq,PAPER on R4

Paper with Auguste

Area 1

There is a mono equil-Tri of size… OPT

PART VI: ROTH'S THEOREM

History of VDW bounds

Roth's Theorem

Roth's Theorem by Kelin

PART VII: MISC

Material Not Covered

Generalized and Geom Ram Nums for cycles

Ramsey Logic Conferenece

Anti-Ramsey Mult

Cycles

Framsey

New Proof Shelah

Rado with constants

Progressions ERT

Rainbow Saturation

Gen Ramsey

Erdos-Sachs Reg-Girth paper in German

Erdos-Sachs Reg-Girth paper, ‘‘translated’’ into English

Sauer Reg-Girth paperh

Erdos-Kakaatoni paper