Special Issue "Graph-Theoretic Problems and Their New Applications"

A special issue of Mathematics (ISSN 2227-7390).

Deadline for manuscript submissions: 31 January 2020

Special Issue Editor

Guest Editor
Prof. Dr. Frank Werner

Otto-von-Guericke-Universität, Fakultät für Mathematik, Magdeburg, Germany
Website | E-Mail
Interests: discrete optimization; operations research; scheduling; graph theory; manufacturing systems

Special Issue Information

Dear Colleagues,

Nowadays, graph theory plays a vital role in many disciplines. We invite you to submit your latest original research results in all aspects of graph theory to this Special Issue. We are looking both for new and innovative approaches for traditional graph-theoretic problems and well as for new applications of graph theory in emerging fields, such as in network security, computer science and data analysis, bioinformatics, operations research, engineering and manufacturing, physics and chemistry, linguistics, or social sciences. Both theoretical results, as well as new graph algorithms, with investigations of their computational complexity will be considered. Below, we give an exemplary, but not exhaustive, list of potential subjects for submissions to this Special Issue.

Prof. Dr. Frank Werner
Guest Editor

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All papers will be peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

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. Mathematics is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 350 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • Deterministic, randomized, exact and approximative graph algorithms
  • Paths, cycles, and trees
  • Network theory
  • Graph labeling
  • Graph coloring
  • Symmetric graphs
  • Polyhedral graphs
  • Topological indices
  • Domination in graphs
  • Applications of graph theory

Published Papers (1 paper)

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Research

Open AccessArticle Kempe-Locking Configurations
Mathematics 2018, 6(12), 309; https://doi.org/10.3390/math6120309
Received: 27 October 2018 / Revised: 28 November 2018 / Accepted: 4 December 2018 / Published: 7 December 2018
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Abstract
The 4-color theorem was proved by showing that a minimum counterexample cannot exist. Birkhoff demonstrated that a minimum counterexample must be internally 6-connected. We show that a minimum counterexample must also satisfy a coloring property that we call Kempe-locking. The novel idea explored
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The 4-color theorem was proved by showing that a minimum counterexample cannot exist. Birkhoff demonstrated that a minimum counterexample must be internally 6-connected. We show that a minimum counterexample must also satisfy a coloring property that we call Kempe-locking. The novel idea explored in this article is that the connectivity and coloring properties are incompatible. We describe a methodology for analyzing whether an arbitrary planar triangulation is Kempe-locked. We provide a heuristic argument that a fundamental Kempe-locking configuration must be of low order and then perform a systematic search through isomorphism classes for such configurations. All Kempe-locked triangulations that we discovered have two features in common: (1) they are Kempe-locked with respect to only a single edge, say x y , and (2) they have a Birkhoff diamond with endpoints x and y as a subgraph. On the strength of our investigations, we formulate a plausible conjecture that the Birkhoff diamond is the only fundamental Kempe-locking configuration. If true, this would establish that the connectivity and coloring properties of a minimum counterexample are indeed incompatible. It would also imply the appealing conclusion that the Birkhoff diamond configuration alone is responsible for the 4-colorability of planar triangulations. Full article
(This article belongs to the Special Issue Graph-Theoretic Problems and Their New Applications)
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