The well-known Chvátal-Erdős theorem states that if the stability number α of a graph G is not greater than its connectivity then G is hamiltonian. In 1974 Erdős showed that if, additionally, the order of the graph is sufficiently large with respect to α, then G is pancyclic. His proof is based on the properties of cycle-complete graph Ramsey numbers. In this paper we show that a similar result...

Applic~atiori codes wliilblg ac,hievr performance f;lr Itw than tht, iidvertist~tl c,apabilities of cxistiug archit,tytnrcs, and this pmble~ii is worsening with irlc,reasingly-I)arallcl machines. For large-scale nunlorical ilpplic~at,iorls, stencil opcratioris oftm iiriposc the grcat,cr part of the wmputat,ional cost, ant1 the primary sources of incfficic3icy arc thr costs of lllrssagc passing ...

A graph G is pancyclic if G includes cycles of all lengths and G is edge-pancyclic if each edge lies on cycles of all lengths. A bipartite graph is edge-bipancyclic if each edge lies on cycles of every even length from 4 to |V (G)|. Two cycles with the same length m, C1 = ⟨u1, u2, · · · , um, u1⟩ and C2 = ⟨v1, v2, · · · , vm, v1⟩ passing through an edge (x, y) are independent with respect to th...

Let r be a finite connecied regular bipartite 2-arc transitive graph. It is shown that r is a cover of a possibly smaller graph :E, which is also connecied and regular of the same valency as r, and there is a subgroup G of Aut :E such that G is 2-arc transitive on :E and every nontrivial normal subgroup of G has at most two orbits on vertices. Such graphs :E for which the subgroup G has an abel...

A tournament T = (V,A) is a directed graph in which there is exactly one arc between every pair of distinct vertices. Given a digraph on n vertices and an integer parameter k, the Feedback Arc Set problem asks whether the given digraph has a set of k arcs whose removal results in an acyclic digraph. The Feedback Arc Set problem restricted to tournaments is known as the k-Feedback Arc Set in Tou...

We fair and ®t planar point sets by minimal-energy arc splines. The fairing process consists of two steps: computing the optimal tangents for curve interpolation and adjusting the point positions by smoothing the discrete curvatures. To ®t the point set with minimal-energy arc curve, a simple linear algorithm is given for computing the optimal tangents. The discrete curvatures derived from the ...

Given a tournament T , let h(T ) be the smallest integer k such that every arc-coloring of T with k or more colors produces at least one out-directed spanning tree of T with no pair of arcs with the same color. In this paper we give the exact value of h(T ).

The relationship between the cuprate pseudogap (Δ(p)) and superconducting gap (Δ(s)) remains an unsolved mystery. Here, we present a temperature- and doping-dependent tunneling study of submicron Bi(2)Sr(2)CaCu(2)O(8+δ) intrinsic Josephson junctions, which provides a clear evidence that Δ(s) closes at a temperature T(c) (0) well above the superconducting transition temperature T(c) but far belo...

In many application areas where graphical models are used and where their structure is learned from data, the end goal is neither prediction nor density estimation. Rather, it is the uncovering of discrete relationships between entities. For example, in computational biology, one may be interested in discovering which proteins within a large set of proteins interact with one another. In these p...

Exercise 2 (Producer/Consumer). A producer/consumer system gathers two types of processes: producers who can make the actions produce (p) or deliver (d), and consumers with the actions receive (r) and consume (c). All the producers and consumers communicate through a single unordered channel. 1. Model a producer/consumer system with two producers and three consumers. How can you modify this sys...