The acyclic polynomial of a graph.
The adaptation of the -means algorithm to solving the multiple ellipses detection problem by using an initial approximation obtained by the DIRECT global optimization algorithm
We consider the multiple ellipses detection problem on the basis of a data points set coming from a number of ellipses in the plane not known in advance, whereby an ellipse is viewed as a Mahalanobis circle with center , radius , and some positive definite matrix . A very efficient method for solving this problem is proposed. The method uses a modification of the -means algorithm for Mahalanobis-circle centers. The initial approximation consists of the set of circles whose centers are determined...
The additive complements of primes and Goldbach's problem
We extend two results of Ruzsa and Vu on the additive complements of primes.
The adjacency graphs of a complex
The admissable trace problem for E-unitary inverse semigroups.
The algebraic connectivity of two trees connected by an edge of infinite weight.
The algebraic multiplicity of the number zero in the spectrum of a bipartite graph
The all-paths transit function of a graph
A transit function on a set is a function satisfying the axioms , and , for all . The all-paths transit function of a connected graph is characterized by transit axioms.
The alternating sign matrix polytope.
The Analysis of a Nested Dissection Algorithm.
The Apollonian decay of beer foam bubble size distribution and the lattices of Young diagrams and their correlated mixing functions.
The arc-width of a graph.
The assignment problem with three job categories
The asymptotic behavior of elementary symmetric functions on a probability distribution.
The asymptotic number of set partitions with unequal block sizes.
The automorphism group of the random lattice is not amenable
We prove that the automorphism group of the random lattice is not amenable, and we identify the universal minimal flow for the automorphism group of the random distributive lattice.
The average order of a permutation.
The Balanced Decomposition Number of TK4 and Series-Parallel Graphs
A balanced colouring of a graph G is a colouring of some of the vertices of G with two colours, say red and blue, such that there is the same number of vertices in each colour. The balanced decomposition number f(G) of G is the minimum integer s with the following property: For any balanced colouring of G, there is a partition V (G) = V1 ∪˙ · · · ∪˙ Vr such that, for every i, Vi induces a connected subgraph of order at most s, and contains the same number of red and blue vertices. The function f(G)...
The basis number of some special non-planar graphs
The basis number of a graph was defined by Schmeichel to be the least integer such that has an -fold basis for its cycle space. He proved that for , the basis number of the complete bipartite graph is equal to 4 except for , and with . We determine the basis number of some particular non-planar graphs such as and , , and -cages for , and the Robertson graph.
The b-chromatic number of power graphs.