Counting unrooted maps using tree-decomposition.
Cubic Cayley graphs with small diameter.
Cyclic sieving phenomenon in non-crossing connected graphs.
Decomposing complete graphs into cubes
This paper concerns when the complete graph on n vertices can be decomposed into d-dimensional cubes, where d is odd and n is even. (All other cases have been settled.) Necessary conditions are that n be congruent to 1 modulo d and 0 modulo . These are known to be sufficient for d equal to 3 or 5. For larger values of d, the necessary conditions are asymptotically sufficient by Wilson’s results. We prove that for each odd d there is an infinite arithmetic progression of even integers n for which...
Dénombrements de chemins dans soumis à contraintes
Dénombrements des cycles hamiltoniens de et empruntant ou évitant des arêtes données
Descents in noncrossing trees.
Direct enumeration of chiral and achiral graphs of a polyheterosubstituted monocyclic cycloalkane.
Dürer polyhedra: the dark side of melancholia
Dürer's engraving Melencolia I famously includes a perspective view of a solid polyhedral block of which the visible portion is an 8-circuit bounding a pentagon-triple+triangle patch. The polyhedron is usually taken to be a cube truncated on antipodal corners, but an infinity of others are compatible with the visible patch. Construction of all cubic polyhedra compatible with the visible portion (i.e., Dürer Polyhedra) is discussed, explicit graphs and symmetries are listed for small cases ( ≤ 18...
Edge Dominating Sets and Vertex Covers
Bipartite graphs with equal edge domination number and maximum matching cardinality are characterized. These two parameters are used to develop bounds on the vertex cover and total vertex cover numbers of graphs and a resulting chain of vertex covering, edge domination, and matching parameters is explored. In addition, the total vertex cover number is compared to the total domination number of trees and grid graphs.
Efficient counting and asymptotics of -noncrossing tangled diagrams.
Ein neuer Algorithmus zur Bestimmung einer basis von unabhängigen elementarkreisen in einem stark zusammenhängenden Graphen
Eine Benutzung der Zahlenzerlegung zur Bestimmung der Anzahl unisomorpher Zyklen in -Turnieren
Elevation of a graph
Enumerating all Hamilton cycles and bounding the number of Hamilton cycles in 3-regular graphs.
Enumeration and asymptotic properties of unlabeled outerplanar graphs.
Énumération des cartes pointées sue la bouteille de Klein
Enumeration of binary trees and universal types.
Enumeration of graphs maximal with respect to connectivity
Enumeration of Hamiltonian circuits in rectangular grids.