Papers Commemorating the Fiftieth Southeastern International Conference on Combinatorics, Graph Theory, and Computing (SEICCGTC 2019)

A special issue of Algorithms (ISSN 1999-4893).

Deadline for manuscript submissions: closed (30 June 2019) | Viewed by 15379

Special Issue Editors


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Guest Editor
Department of Mathematical Sciences, Florida Atlantic University, Boca Raton, FL SE43, USA
Interests: combinatorics and applications; finite groups; artificial intelligence

E-Mail Website
Guest Editor
Department of Mathematical Sciences, Florida Atlantic University, Boca Raton, FL SE43, USA
Interests: graph theory; combinatorics; mathematical problem solving

Special Issue Information

Dear Colleagues,

This Special Issue commemorates the 50th anniversary of the Southeastern International Conference on Combinatorics, Graph Theory and Computing. It is to be a collection of papers reflecting the intersections of the mathematics presented over the past fifty years at the conference and the areas of interest of the journal. It is not to be a collection of papers presented at the 50th Conference. We are soliciting papers reporting on current research in appropriate areas, as well as more retrospective papers. Reports on areas in which progress has been reported at the Conference over a period of time are most appropriate. We would expect submissions in such areas as:

  • Algorithms for graph drawing, coloring and labeling
  • Scheduling algorithms
  • Network design and construction
  • Computation of graph invariants and combinatorial numbers
  • Characteristics of networks
  • Finding dominating sets in graphs
  • Constructing error-correcting codes
  • Automated discovery in combinatorial optimization
  • Algorithms for parallel or quantum computation
  • Combinatorial search algorithms
  • Game playing algorithms
  • Covering and packing
  • Routing
  • Constructing families of designs

Prof. Dr. Frederick Hoffman
Prof. Dr. Stephen C. Locke
Guest Editors

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Published Papers (4 papers)

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Research

3 pages, 181 KiB  
Article
What Do a Longest Increasing Subsequence and a Longest Decreasing Subsequence Know about Each Other?
by Elizabeth J. Itskovich and Vadim E. Levit
Algorithms 2019, 12(11), 237; https://doi.org/10.3390/a12110237 - 7 Nov 2019
Cited by 1 | Viewed by 3962
Abstract
As a kind of converse of the celebrated Erdős–Szekeres theorem, we present a necessary and sufficient condition for a sequence of length n to contain a longest increasing subsequence and a longest decreasing subsequence of given lengths x and y, respectively. Full article
10 pages, 249 KiB  
Article
Cyclotomic Trace Codes
by Dean Crnković, Andrea Švob and Vladimir D. Tonchev
Algorithms 2019, 12(8), 168; https://doi.org/10.3390/a12080168 - 13 Aug 2019
Cited by 2 | Viewed by 3933
Abstract
A generalization of Ding’s construction is proposed that employs as a defining set the collection of the sth powers ( s 2 ) of all nonzero elements in G F ( p m ) , where p 2 is prime. [...] Read more.
A generalization of Ding’s construction is proposed that employs as a defining set the collection of the sth powers ( s 2 ) of all nonzero elements in G F ( p m ) , where p 2 is prime. Some of the resulting codes are optimal or near-optimal and include projective codes over G F ( 4 ) that give rise to optimal or near optimal quantum codes. In addition, the codes yield interesting combinatorial structures, such as strongly regular graphs and block designs. Full article
13 pages, 260 KiB  
Article
Equisum Partitions of Sets of Positive Integers
by Roger B. Eggleton
Algorithms 2019, 12(8), 164; https://doi.org/10.3390/a12080164 - 11 Aug 2019
Viewed by 3270
Abstract
Let V be a finite set of positive integers with sum equal to a multiple of the integer b . When does V have a partition into b parts so that all parts have equal sums? We develop algorithmic constructions which yield positive, [...] Read more.
Let V be a finite set of positive integers with sum equal to a multiple of the integer b . When does V have a partition into b parts so that all parts have equal sums? We develop algorithmic constructions which yield positive, albeit incomplete, answers for the following classes of set V , where n is a given positive integer: (1) an initial interval { a + : a n } ; (2) an initial interval of primes { p : p n } , where is the set of primes; (3) a divisor set { d + : d | n } ; (4) an aliquot set { d + : d | n ,   d < n } . Open general questions and conjectures are included for each of these classes. Full article
18 pages, 320 KiB  
Article
γ-Graphs of Trees
by Stephen Finbow and Christopher M. van Bommel
Algorithms 2019, 12(8), 153; https://doi.org/10.3390/a12080153 - 30 Jul 2019
Cited by 1 | Viewed by 3630
Abstract
For a graph G = ( V , E ) , the γ -graph of G, denoted G ( γ ) = ( V ( γ ) , E ( γ ) ) , is the graph whose vertex set is the [...] Read more.
For a graph G = ( V , E ) , the γ -graph of G, denoted G ( γ ) = ( V ( γ ) , E ( γ ) ) , is the graph whose vertex set is the collection of minimum dominating sets, or γ -sets of G, and two γ -sets are adjacent in G ( γ ) if they differ by a single vertex and the two different vertices are adjacent in G. In this paper, we consider γ -graphs of trees. We develop an algorithm for determining the γ -graph of a tree, characterize which trees are γ -graphs of trees, and further comment on the structure of γ -graphs of trees and its connections with Cartesian product graphs, the set of graphs which can be obtained from the Cartesian product of graphs of order at least two. Full article
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