Hiu-Fai Law, Colin McDiarmid
Published 2012-10-04Version 1
We consider numbers and sizes of independent sets in graphs with minimum degree at least $d$, when the number $n$ of vertices is large. In particular we investigate which of these graphs yield the maximum numbers of independent sets of different sizes, and which yield the largest random independent sets. We establish a strengthened form of a conjecture of Galvin concerning the first of these topics.
Graphs without proper subgraphs of minimum degree 3 and short cycles
On a Greedy 2-Matching Algorithm and Hamilton Cycles in Random Graphs with Minimum Degree at Least Three
Triangulated map with minimum degree four is Hamiltonian
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