An entropy proof of the Kahn-Lovász theorem.
An enumeration theorem for rooted graphs
An Enumerative Problem in Threshold Logic
An equational basis in four variables for the three-element tournament
An equivalence criterion for 3-manifolds.
Within geometric topology of 3-manifolds (with or without boundary), a representation theory exists, which makes use of 4-coloured graphs. Aim of this paper is to translate the homeomorphism problem for the represented manifolds into an equivalence problem for 4-coloured graphs, by means of a finite number of graph-moves, called dipole moves. Moreover, interesting consequences are obtained, which are related with the same problem in the n-dimensional setting.
An estimate for Frobenius' Diophantine problem in three dimensions.
An Eulerian partner for inversions.
An even side analogue of Room squares.
An evolutionary formulation of the crossing number problem.
An exact performance bound for an time greedy matching procedure.
An Exchange Property For The Submodular Systems.
An explanatory bijection of some properties of bridges. (Une bijection explicative de plusieurs propriétés de ponts.)
An exploration of the permanent-determinant method.
An extension of a criterion for unimodality.
An extension of Franklin's bijection.
An Extension of Kotzig’s Theorem
In 1955, Kotzig proved that every 3-connected planar graph has an edge with the degree sum of its end vertices at most 13, which is tight. An edge uv is of type (i, j) if d(u) ≤ i and d(v) ≤ j. Borodin (1991) proved that every normal plane map contains an edge of one of the types (3, 10), (4, 7), or (5, 6), which is tight. Cole, Kowalik, and Škrekovski (2007) deduced from this result by Borodin that Kotzig’s bound of 13 is valid for all planar graphs with minimum degree δ at least 2 in which every...
An extension of Kotzig’s theorem on the minimum weight of edges in -polytopes
An extension of matroid rank submodularity and the -Rayleigh property.
An extension of the exponential formula in enumerative combinatorics.
An extension of the Foata map to standard Young tableaux.