In 1978 Thomassen asked whether planar hypohamiltonian oriented graphs exist. Infinite families of such have since been described but for infinitely many n it remained an open question order this paper we develop new methods constructing digraphs, which, combined with efficient graph generation algorithms, enable us to fully characterise the orders which Our novel also led discover smallest and...

A graph is said to be planar if it can be drawn on the plane in such a way that no two of its edges cross. Given a graph G = (V,E) with vertex set V and edge set E, the objective of graph planarization is to find a minimum cardinality subset of edges F ⊆ E such that the graph G = (V,E \ F ), resulting from the removal of the edges in F from G, is planar. This problem is also known as the maximu...

A graph G is a support for a hypergraph H = (V,S) if the vertices of G correspond to the vertices of H such that for each hyperedge Si ∈ S the subgraph of G induced by Si is connected. G is a planar support if it is a support and planar. Johnson and Pollak [11] proved that it is NPcomplete to decide if a given hypergraph has a planar support. In contrast, there are lienar time algorithms to tes...

In this paper we study the page number of upward planar directed acyclic graphs. We prove that: (1) the page number of any n-vertex upward planar triangulation G whose every maximal 4-connected component has page number k is at most min{O(k logn), O(2)}; (2) every upward planar triangulation G with o( n logn ) diameter has o(n) page number; and (3) every upward planar triangulation has a vertex...

All lattices are assumed to be finite. Björner [2] has shown that a dismantlable (see Rival, [5]) lattice L is Cohen-Macaulay (see [6] for definition) if and only if L is ranked and interval-connected. A lattice is planar if its Hasse diagram can be drawn in the plane with no edges crossing. Baker, Fishburn and Roberts have shown that planar lattices are dismantlable, see [1]. Lexicographically...

We consider the Stokes resolvent problem in a two-dimensional bounded Lipschitz domain $\Omega$ subject to homogeneous Dirichlet boundary conditions. prove $\mathrm{L}^p$-resolvent estimates for $p$ satisfying condition $\lvert 1 / p - 2 \rvert < 4 + \varepsilon$ some $\varepsilon > 0$. further show that operator admits property of maximal regularity and its $\mathrm{H}^{\infty}$-calculus is bo...

Open problems submitted to the 2nd Canadian Discrete and Algorithmic Mathematics Conference will be held on May 25-28, 2009, at the Centre de recherches mathématiques in Montréal, Canada. put brief summary here Comments and questions of a technical nature about a particular problem should be sent to the correspondent for that problem. Please send other comments and information about partial or ...

A simple graph is said to be reflexive if its second largest eigenvalue does not exceed 2. The property λ2 ≤ 2 is a hereditary one, i.e. any induced subgraph of a reflexive graph preserves this property and that is why reflexive graphs are usually represented by maximal graphs within a given class. Bicyclic graphs whose two cycles have a common path are called θ-graphs. We consider classes of m...

AbstructCommercially available modular fixturing systems typically include a lattice of holes with precise spacing and an assortment of precision locating and clamping modules that can be rigidly attached to the lattice. Currently, machinists manually design a suitable arrangement of these modules to hold a given part. This requires expertise and can delay production. Futhermore, a machinist ma...

We investigated maximal Prym varieties on finite fields by attaining their upper bounds on the number of rational points. This concept gave us a motivation for defining a generalized definition of maximal curves i.e. maximal morphisms. By MAGMA, we give some non-trivial examples of maximal morphisms that results in non-trivial examples of maximal Prym varieties.