3,225 research outputs found
Restricted Size Ramsey Number for Path of Order Three Versus Graph of Order Five
Let and be simple graphs. The Ramsey number for a pair of graph and is the smallest number such that any red-blue coloring of edges of contains a red subgraph or a blue subgraph . The size Ramsey number for a pair of graph and is the smallest number such that there exists a graph with size satisfying the property that any red-blue coloring of edges of contains a red subgraph or a blue subgraph . Additionally, if the order of in the size Ramsey number is , then it is called the restricted size Ramsey number. In 1983, Harary and Miller started to find the (restricted) size Ramsey number for any pair of small graphs with order at most four. Faudree and Sheehan (1983) continued Harary and Miller\u27s works and summarized the complete results on the (restricted) size Ramsey number for any pair of small graphs with order at most four. In 1998, Lortz and Mengenser gave both the size Ramsey number and the restricted size Ramsey number for any pair of small forests with order at most five. To continue their works, we investigate the restricted size Ramsey number for a path of order three versus connected graph of order five
The DLV System for Knowledge Representation and Reasoning
This paper presents the DLV system, which is widely considered the
state-of-the-art implementation of disjunctive logic programming, and addresses
several aspects. As for problem solving, we provide a formal definition of its
kernel language, function-free disjunctive logic programs (also known as
disjunctive datalog), extended by weak constraints, which are a powerful tool
to express optimization problems. We then illustrate the usage of DLV as a tool
for knowledge representation and reasoning, describing a new declarative
programming methodology which allows one to encode complex problems (up to
-complete problems) in a declarative fashion. On the foundational
side, we provide a detailed analysis of the computational complexity of the
language of DLV, and by deriving new complexity results we chart a complete
picture of the complexity of this language and important fragments thereof.
Furthermore, we illustrate the general architecture of the DLV system which
has been influenced by these results. As for applications, we overview
application front-ends which have been developed on top of DLV to solve
specific knowledge representation tasks, and we briefly describe the main
international projects investigating the potential of the system for industrial
exploitation. Finally, we report about thorough experimentation and
benchmarking, which has been carried out to assess the efficiency of the
system. The experimental results confirm the solidity of DLV and highlight its
potential for emerging application areas like knowledge management and
information integration.Comment: 56 pages, 9 figures, 6 table
Toward a First-Principles Calculation of Electroweak Box Diagrams
We derive a Feynman-Hellmann theorem relating the second-order nucleon energy
shift resulting from the introduction of periodic source terms of
electromagnetic and isovector axial currents to the parity-odd nucleon
structure function . It is a crucial ingredient in the theoretical study
of the and box diagrams that are known to suffer from
large hadronic uncertainties. We demonstrate that for a given , one only
needs to compute a small number of energy shifts in order to obtain the
required inputs for the box diagrams. Future lattice calculations based on this
approach may shed new light on various topics in precision physics including
the refined determination of the Cabibbo-Kobayashi-Maskawa matrix elements and
the weak mixing angle.Comment: Version to appear in PR
Curves in R^d intersecting every hyperplane at most d+1 times
By a curve in R^d we mean a continuous map gamma:I -> R^d, where I is a
closed interval. We call a curve gamma in R^d at most k crossing if it
intersects every hyperplane at most k times (counted with multiplicity). The at
most d crossing curves in R^d are often called convex curves and they form an
important class; a primary example is the moment curve
{(t,t^2,...,t^d):t\in[0,1]}. They are also closely related to Chebyshev
systems, which is a notion of considerable importance, e.g., in approximation
theory. We prove that for every d there is M=M(d) such that every at most d+1
crossing curve in R^d can be subdivided into at most M convex curves. As a
consequence, based on the work of Elias, Roldan, Safernova, and the second
author, we obtain an essentially tight lower bound for a geometric Ramsey-type
problem in R^d concerning order-type homogeneous sequences of points,
investigated in several previous papers.Comment: Corrected proof of Lemma 3.
Restricted Size Ramsey Number for Matching versus Tree and Triangle Unicyclic Graphs of Order Six
Let F, G, and H be simple graphs. The graph F arrows (G,H) if for any red-blue coloring on the edge of F, we find either a red-colored graph G or a blue-colored graph H in F. The Ramsey number r(G,H) is the smallest positive integer r such that a complete graph Kr arrows (G,H). The restricted size Ramsey number r∗(G,H) is the smallest positive integer r∗ such that there is a graph F, of order r(G,H) and with the size r∗, satisfying F arrows (G,H). In this paper we give the restricted size Ramsey number for a matching of two edges versus tree and triangle unicyclic graphs of order six
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