A multivariate Lagrange inversion formula for asymptotic calculations.
A natural extension of Catalan numbers.
A natural series for the natural logarithm.
A necessary and sufficient eigenvector condition for a connected graph to be bipartite.
A Neighborhood Condition for Fractional ID-[A, B]-Factor-Critical Graphs
Let G be a graph of order n, and let a and b be two integers with 1 ≤ a ≤ b. Let h : E(G) → [0, 1] be a function. If a ≤ ∑e∋x h(e) ≤ b holds for any x ∈ V (G), then we call G[Fh] a fractional [a, b]-factor of G with indicator function h, where Fh = {e ∈ E(G) : h(e) > 0}. A graph G is fractional independent-set-deletable [a, b]-factor-critical (in short, fractional ID-[a, b]- factor-critical) if G − I has a fractional [a, b]-factor for every independent set I of G. In this paper, it is proved...
A new algorithm for the four counterfeit coins problem.
A new algorithm for the three counterfeit coins problem.
A new and stronger central sets theorem
Furstenberg's original Central Sets Theorem applied to central subsets of ℕ and finitely many specified sequences in ℤ. In this form it was already strong enough to derive some very strong combinatorial consequences, such as the fact that a central subset of ℕ contains solutions to all partition regular systems of homogeneous equations. Subsequently the Central Sets Theorem was extended to apply to arbitrary semigroups and countably many specified sequences. In this paper we derive a new version...
A new approach to chordal graphs
By a chordal graph is meant a graph with no induced cycle of length . By a ternary system is meant an ordered pair , where is a finite nonempty set, and . Ternary systems satisfying certain axioms (A1)–(A5) are studied in this paper; note that these axioms can be formulated in a language of the first-order logic. For every finite nonempty set , a bijective mapping from the set of all connected chordal graphs with onto the set of all ternary systems satisfying the axioms (A1)–(A5) is...
A new approach to -Bernoulli numbers and -Bernoulli polynomials related to -Bernstein polynomials.
A New Approach to the Dynamic Maintenance of Maximal Points in a Plane.
A new approach to the Dyson coefficients.
A new bound for the spectral radius of Brualdi-Li matrices
Let B2m denote the Brualdi-Li matrix of order 2m, and let ρ2m = ρ(B2m ) denote the spectral radius of the Brualdi-Li Matrix. Then [...] . where m > 2, e = 2.71828 · · · , [...] and [...] .
A new bound on the domination number of graphs with minimum degree two.
A new characterization of the maximum genus of a graph
A New Characterization of Unichord-Free Graphs
Unichord-free graphs are defined as having no cycle with a unique chord. They have appeared in several papers recently and are also characterized by minimal separators always inducing edgeless subgraphs (in contrast to characterizing chordal graphs by minimal separators always inducing complete subgraphs). A new characterization of unichord-free graphs corresponds to a suitable reformulation of the standard simplicial vertex characterization of chordal graphs.
A new class of enumeration problems
A new class of infinite products, and Euler's totient.
A new class of -Fibonacci polynomials.
A new class of symmetric functions.