The energy of a graph

On a Problem in Combinations

Keccak sponge function family main document

Un code pour les graphes planaires et ses applications.

A graph is planar if it can be embedded in the plane, or in the sphere, so that no two edges cross at an interior point A planar graph together with a particular embedding is called a map There is a rich theory of counting maps, started by Tutte in the 1960's However, in this paper we are interested in counting graphs as combinatorial objects, regardless of how many nonequivalent topological embeddings they may have As we are going to see, this makes the counting considerably more difficult

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Asymptotic enumeration and limit laws of planar graphs

The Oberwolfach problem and factors of uniform odd length cycles

The enumeration of c-nets via quadrangulations

The existence of C k -factorizations of K 2 n - F

Hanani triple systems onv≡1 (mod 6) elements are Steiner triple systems having (v−1)/2 pairwise disjoint almost parallel classes (sets of pairwise disjoint triples that spanv−1 elements), and the remaining triples form a partial parallel class. Hanani triple systems are one natural analogue of the Kirkman triple systems onv≡3 (mod 6) elements, which form the solution of the celebrated Kirkman schoolgirl problem. We prove that a Hanani triple system exists for allv≡1 (mod 6) except forv ∈ {7, 13}.

Paul J. Schellenberg

Papers

The Oberwolfach problem and factors of uniform odd length cycles

The enumeration of c-nets via quadrangulations

The existence of C k -factorizations of K 2 n - F

Hanani triple systems

On the existence of frames