Author(s): Hunter Saint Clair Snevily
Series: PhD thesis at University of Illinois at Urbana-Champaign
Year: 1991
Contents
1 Chvétal’sConjectur-e................L ....................... 1
1.1 Chvétal’s Conjecture .................................... 2
1.2 Latent Subsets of Intersecting Families .......................... 8
2 Intersecting Families with Restricted Intersection Values ............... 13
2.1 Introduction ......................................... 14
2.2 The Case n 5 2k + 3 .................................... 16
2.3 The Case When 1: Is Sufficiently Large .......................... 17
2.4 On Possible Counterexamples ............................... 22
2.5 Conclusions and Further Problems ............................ 25
e
3 Cyclically Invariant Matchings of the Middle Level of the Boolean Lattice . . . 27
3.1 Introduction ......................................... 28
3.2 Lexical and Modular Matchings ........... . ................. 28
3.3 Distribution Vectors .................................... 40
3.4 Orbits and Uniqueness of i-Modular Matchings ..................... 42
3.5 Tweaking.......................... ................ 50
3.6 Labeling Zeros in Cyclic 0-1 Arrangements . . .. ..... i ............... 52
3.7 Odd Graph Matchings ................................... 54
3.8 a-Invariant Hamiltonian Cycles .............................. 55
3.9 A Strong Form of the Cycle Lemma ........................... 58
4 Graph Decompositions and a-labelings ............................ 63
4.1 Introduction ......................................... 64
4.2 On Prisms D,’; and Cm1 x Cm, x - - - x Cm, ....................... 67
4.3 Decompositions into Nonisomorphic Trees ........................ 73
4.4 a-labelings ......................................... 77
Bibliography ............................................... 88
Vita ..................................................... 93
