Demetres Christofides

Multiple unicasts, graph guessing games, and non-Shannon inequalities

Guessing games for directed graphs were introduced by Riis [8] for studying multiple unicast network coding problems. It can be shown that protocols for a multiple unicast network can be directly converted into a strategy for a guessing game. The performance of the optimal strategy for a graph is measured by the guessing number, and this number can be bounded from above using information inequalities. Christofides and Markstrom [4] developed a guessing strategy for undirected graphs based on the fractional clique cover, and they conjectured that this strategy is optimal for undirected graphs. In this paper we disprove this conjecture. We also provide an example of an undirected graph for which non-Shannon inequalities provide a better bound on the guessing number than Shannon inequalities. Finally, we construct a counterexample to a conjecture we raised during our work which we referred to as the Superman conjecture.

A Semiexact Degree Condition for Hamilton Cycles in Digraphs

We show that for each

Finding Hamilton cycles in robustly expanding digraphs

\beta > 0

Hamilton cycles in dense vertex-transitive graphs

, every digraph

A Note on Hitting Maximum and Maximal Cliques With a Stable Set

G

Random Latin square graphs

of sufficiently large order

Graph Guessing Games and Non-Shannon Information Inequalities

n

The thresholds for diameter 2 in random Cayley graphs

whose outdegree and indegree sequences

A fast algorithm for the gas station problem

d_1^+ \leq \cdots \leq d_n^+

First-Order Convergence and Roots

and