A new proof of a characterization of the set of all geodesics in a connected graph
A new proof of a theorem of Dirac on the number of edges in critical graphs.
A new proof of some identities of Bressoud.
A new proof of the four-colour theorem.
A new proof of the -Dixon identity
We give a new and elementary proof of Jackson’s terminating -analogue of Dixon’s identity by using recurrences and induction.
A New Proof of the Szeged-Wiener Theorem
A New Proof that 4-Connected Planar Graphs are Hamiltonian-Connected
We prove a theorem guaranteeing special paths of faces in 2-connected plane graphs. As a corollary, we obtain a new proof of Thomassen’s theorem that every 4-connected planar graph is Hamiltonian-connected.
A new spectral method for determining the number of spanning trees.
A new sphere packing in 20 dimensions.
A new statistic on linear and circular -mino arrangements.
A new triple sum combinatorial identity.
A new upper bound for the chromatic number of a graph
Let G be a graph of order n with clique number ω(G), chromatic number χ(G) and independence number α(G). We show that χ(G) ≤ [(n+ω+1-α)/2]. Moreover, χ(G) ≤ [(n+ω-α)/2], if either ω + α = n + 1 and G is not a split graph or α + ω = n - 1 and G contains no induced .
A new upper bound for the Laplacian spectral radius of a graph.
A new upper bound on the total domination number of a graph.
A `nice' bijection for a content formula for skew semistandard Young tableaux.
A non graph theory approach to Ulam's conjecture
A non-differentiablity result for the inversion operator between Sobolev spaces.
A Nonuniform Matroid Which Violates the Isotopy Conjecture.
A normalization formula for the Jack polynomials in superspace and an identity on partitions.
A not on dominating set with Maple.