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

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Special Issue Editors

Prof. Dr. Frederick Hoffman

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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

Dr. Stephen C. Locke

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 50^th 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 50^th 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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Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Algorithms is an international peer-reviewed open access monthly journal published by MDPI.

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Published Papers (4 papers)

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Research

3 pages, 181 KiB

Open AccessArticle

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 3928

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

(This article belongs to the Special Issue Papers Commemorating the Fiftieth Southeastern International Conference on Combinatorics, Graph Theory, and Computing (SEICCGTC 2019))

10 pages, 249 KiB

Open AccessArticle

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 3899

Abstract

A generalization of Ding’s construction is proposed that employs as a defining set the collection of the sth powers (

s \geq 2

) of all nonzero elements in

G F (p^{m})

, where

p \geq 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 \geq 2

) of all nonzero elements in

G F (p^{m})

, where

p \geq 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

(This article belongs to the Special Issue Papers Commemorating the Fiftieth Southeastern International Conference on Combinatorics, Graph Theory, and Computing (SEICCGTC 2019))

13 pages, 260 KiB

Open AccessArticle

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 3240

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 \in ℤ^{+} : a \leq n}

; (2) an initial interval of primes

{p \in ℙ : p \leq n}

, where

ℙ

is the set of primes; (3) a divisor set

{d \in ℤ^{+} : d | n}

; (4) an aliquot set

{d \in ℤ^{+} : d | n, d < n}

. Open general questions and conjectures are included for each of these classes. Full article

(This article belongs to the Special Issue Papers Commemorating the Fiftieth Southeastern International Conference on Combinatorics, Graph Theory, and Computing (SEICCGTC 2019))

18 pages, 320 KiB

Open AccessArticle

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 3612

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

(This article belongs to the Special Issue Papers Commemorating the Fiftieth Southeastern International Conference on Combinatorics, Graph Theory, and Computing (SEICCGTC 2019))

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