Problems in Combinatorics and Graph Theory

Preface.................................................................................  6
Contents................................................................................  8
Glossary of terms used.................................................................. 10
1 STATEMENT OF PROBLEMS................................................................. 20
 1.1 COMBINATORIAL IDENTITIES........................................................ 22
 1.2 THE PRINCIPLE OF INCLUSION AND EXCLUSION and INVERSION FORMULAS................. 29
 1.3 STIRLING, BELL, FIBONACCI AND CATALAN NUMBERS................................... 34
 1.4 PROBLEMS IN COMBINATORIAL SET THEORY........................................... 41
 1.5 PARTITIONS OF INTEGERS.......................................................... 49
 1.6 TREES........................................................................... 52
 1.7 PARITY.......................................................................... 58
 1.8 CONNECTEDNESS................................................................... 60
 1.9 EXTREMAL PROBLEMS FOR GRAPHS AND NETWORKS....................................... 64
 1.10 COLORING PROBLEMS.............................................................. 71
 1.11 HAMILTONIAN PROBLEMS........................................................... 75
 1.12 PERMUTATIONS................................................................... 77
 1.13 THE NUMBER OF CLASSES OF CONFIGURATIONS RELATIVE TO A GROUP OF PERMUTATIONS.... 81
 1.14 PROBLEMS OF RAMSEY TYPE........................................................ 84
2 SOLUTIONS............................................................................. 88
3 BIBLIOGRAPHY..........................................................................354