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Linear forests and ordered cycles

Guantao Chen, Ralph J. Faudree, Ronald J. Gould, Michael S. Jacobson, Linda Lesniak, Florian Pfender (2004)

Discussiones Mathematicae Graph Theory

A collection L = P ¹ ∪ P ² ∪ . . . ∪ P t (1 ≤ t ≤ k) of t disjoint paths, s of them being singletons with |V(L)| = k is called a (k,t,s)-linear forest. A graph G is (k,t,s)-ordered if for every (k,t,s)-linear forest L in G there exists a cycle C in G that contains the paths of L in the designated order as subpaths. If the cycle is also a hamiltonian cycle, then G is said to be (k,t,s)-ordered hamiltonian. We give sharp sum of degree conditions for nonadjacent vertices that imply a graph is (k,t,s)-ordered hamiltonian.

Linear operator identities in quasigroups

Reza Akhtar (2022)

Commentationes Mathematicae Universitatis Carolinae

We study identities of the form L x 0 ϕ 1 ⋯ ϕ n R x n + 1 = R x n + 1 ϕ σ ( 1 ) ⋯ ϕ σ ( n ) L x 0 in quasigroups, where n ≥ 1 , σ is a permutation of { 1 , ... , n } , and for each i , ϕ i is either L x i or R x i . We prove that in a quasigroup, every such identity implies commutativity. Moreover, if σ is chosen randomly and uniformly, it also satisfies associativity with probability approaching 1 as n → ∞ .

Linear programming duality and morphisms

Winfried Hochstättler, Jaroslav Nešetřil (1999)

Commentationes Mathematicae Universitatis Carolinae

In this paper we investigate a class of problems permitting a good characterisation from the point of view of morphisms of oriented matroids. We prove several morphism-duality theorems for oriented matroids. These generalize LP-duality (in form of Farkas' Lemma) and Minty's Painting Lemma. Moreover, we characterize all morphism duality theorems, thus proving the essential unicity of Farkas' Lemma. This research helped to isolate perhaps the most natural definition of strong maps for oriented matroids....

Link homotopy invariants of graphs in R3.

Kouki Taniyama (1994)

Revista Matemática de la Universidad Complutense de Madrid

In this paper we define a link homotopy invariant of spatial graphs based on the second degree coefficient of the Conway polynomial of a knot.

List coloring of complete multipartite graphs

Tomáš Vetrík (2012)

Discussiones Mathematicae Graph Theory

The choice number of a graph G is the smallest integer k such that for every assignment of a list L(v) of k colors to each vertex v of G, there is a proper coloring of G that assigns to each vertex v a color from L(v). We present upper and lower bounds on the choice number of complete multipartite graphs with partite classes of equal sizes and complete r-partite graphs with r-1 partite classes of order two.

Local admissible convergence of harmonic functions on non-homogeneous trees

Massimo A. Picardello (2010)

Colloquium Mathematicae

We prove admissible convergence to the boundary of functions that are harmonic on a subset of a non-homogeneous tree equipped with a transition operator that satisfies uniform bounds suitable for transience. The approach is based on a discrete Green formula, suitable estimates for the Green and Poisson kernel and an analogue of the Lusin area function.

Currently displaying 101 – 120 of 188