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.
A Note on a Bermond's Conjecture
A Note on a Broken-Cycle Theorem for Hypergraphs
Whitney’s Broken-cycle Theorem states the chromatic polynomial of a graph as a sum over special edge subsets. We give a definition of cycles in hypergraphs that preserves the statement of the theorem there
A note on a conjecture on niche hypergraphs
For a digraph , the niche hypergraph of is the hypergraph having the same set of vertices as and the set of hyperedges and there exists a vertex such that or . A digraph is said to be acyclic if it has no directed cycle as a subdigraph. For a given hypergraph , the niche number is the smallest integer such that together with isolated vertices is the niche hypergraph of an acyclic digraph. C. Garske, M. Sonntag and H. M. Teichert (2016) conjectured that for a linear hypercycle...
A note on a distance bound using eigenvalues of the normalized Laplacian matrix.
A note on a Moore bound for graphs embedded in surfaces.