Erdős and Sós proposed a problem of determining the maximum number F (n) of rainbow triangles in 3-edge-colored complete graphs on n vertices. They conjectured that F (n) = F (a)+ F (b) +F (c) +F (d) + abc+ abd+ acd+ bcd, where a+ b+ c+ d = n and a, b, c, d are as equal as possible. We prove that the conjectured recurrence holds for sufficiently large n. We also prove the conjecture for n = 4 f...

We study the number of matching substrings in the pattern matching problem. In general, there can be a quadratic number of matching substrings in the size of a given text. The linearizing restriction enables to find at most a linear number of matching substrings. We first explore two well-known linearizing restriction rules, the longest-match rule and the shortest-match substring search rule, a...

As an application of CCTV Traffic surveillance, retrieval of the number plate from the vehicles is an important dimension, which demands intelligent solution. In this document, template matching block of computer vision toolbox has been used to extract the vehicle number plate. It is assumed that images of the vehicle have been captured at a particular resolution and orientation. It is also ass...

An r-edge coloring of a graph G is a mapping h : E(G) → [r], where h(e) is the color assigned to edge e ∈ E(G). An exact r-edge coloring is an r-edge coloring h such that there exists an e ∈ E(G) with h(e) = i for all i ∈ [r]. Let h be an edge coloring of G. We say G is rainbow if no two edges in G are assigned the same color by h. The anti-Ramsey number, AR(G,n), is the smallest integer r such...

The significant increase in using reservoir simulation models poses significant challenges in the design and calibration of models. Moreover, conventional model calibration, history matching, is usually performed using a trial and error process of adjusting model parameters until a satisfactory match is obtained. In addition, history matching is an inverse problem, and hence it may have non-uni...

A matching is maximal if no other matching contains it as a proper subset. Maximal matchings model phenomena across many disciplines, including applications within chemistry. In this paper, we study maximal matchings in an important class of chemical compounds: polyphenylenes. In particular, we determine the extremal polyphenylene chains in regards to the number of maximal matchings. We also de...