ON THE EMERGENCE OF SMALL CONFIGURATIONS
THE CLASSICS:TURÁN, ERDOS-STONE-SIMONOVITS & RAMSEY
SELF- STUDY
PRELIMINARIES
MANTEL'S THEOREM
TURÁN'S THEOREM
TURÁN DENSITY
SELF STUDY
THRESHOLDS
ERDOS-STONE-SIMONOVITS THM
SUPERSATURATION
COUNTING 4-CYCLES
KOVARI-SÓS-TURÁN THM
DEPENDENT RANDOM CHOICE
RAMSEY'S THEOREM
SELF-STUDY
RAMSEY SUPERSATURATION
FUNDAMENTALS OF THE REGULARITY METHOD
SZEMERÉDI'S REGULARITY LEMMA & ITS APPLICATIONS
REGULARITY METHOD
PROPERTIES OF DENSE REGULAR PAIRS
REGULARITY METHOD
TWO CLASSICAL APPLICATIONS
REGULARITY METHOD
THE COUNTING LEMMA
REGULARITY METHOD
TRIANGLE COUNTING LEMMA
ARITHMETIC PROGRESSIONS
IN DENSE SETS OF INTEGRES
PSEUDORANDOM GRAPHS
(ALMOST) SPANNING STRUCTURES IN GRAPHS
LONG PATHS & HAMILTONICITY OF RANDOM GRAPHS
LONG PATHS IN GRAPHS
HAMILTONICITY IN RANDOM GRAPHS
EXPANSION IN
RANDOM GRAPHS
GRAPH COLOURING
HADWIGER, HAJÓS, AND BEYOND BROOKS
HADWIGER'S CONJECTURE
IN RANDOM GRAPHS
HAJÓS' CONJECTURE
IN RANDOM GRAPHS
SELF STUDY
K3-FREE GRAPHS
BEYOND THE BROOKS BOUND
SPECTRAL GRAPH THEORY
EARLY NOTIONS
ADJACENCY MATRIX
RAYLEIGH'S PRINCIPLE
COURNAT-FISCHER
SPECTRAL THEOREM
PERRON-FROBENIUS
CONNECTIVITY VIA LAPLACIANS
SYMMETRIC MATRICES
LAPLACIANS
EXPANDER MIXING LEMMA