Anders Sune Pedersen, Cand.Scient., Ph.D. (SDU, 24th of January 2011)
Contact information:
Email:
asp@imada.sdu.dk
I shall be (have been) attending the following events:
Algebraic Graph Theory Summer School 2011, Rogla, Slovenia USCS 2011: Applied Functional Programming Kolloquium über Kombinatorik, 11.-12. November 2011, Otto-von-Guericke-Universität, Magdeburg EMS/DMF Joint Mathematical Weekend, Aarhus 5-7 April 2013 MADALGO Summer School on DATA STRUCTURES, August 19-22, 2013 Aarhus UniversityErdös lap number: At Prague Midsummer Combinatorial Workshop XV I attained Erdös lap number 3.
Research interest: Graph Theory and Combinatorics
Mathematical publications (pdf, ps)
Professional activities:
Reviewer for
Referee for
Annals of Combinatorics
Applied Mathematics
Ars Combinatoria
Australasian Journal of Combinatorics
Discrete Applied Mathematics
Discrete Mathematics
Discrete Mathematics, Algorithms and Applications
Discrete Mathematics and Theoretical Computer Science
Discussiones Mathematicae
European Journal of Combinatorics
Electronic Journal of Combinatorics
Filomat
Information Processing Letters
ISAAC -- International Symposium on Algorithms and Computation
Journal of Mathematical Research with Applications
LAGOS -- Latin-American Algorithms, Graphs and Optimization Symposium
Journal of Graph Theory
Mathematica Scandinavica
Miskolc Mathematical Notes
Springer Verlag
Opuscula Mathematica
L. D. Andersen, J. Bang-Jensen, J. Bárat, M. Chiarandini, T. R. Jensen, L. K. Jørgensen, M. Kriesell, A. S. Pedersen, B. Toft (Eds.) (2010). Special issue dedicated to Carsten Thomassen on his 60th birthday, vol. 310 of Discrete Mathematics. [ DOI ]
Technical reports, preprints, manuscripts, news, etc.:
On computational complexity and Gallai-type theorems involving graph domination parameters, preprints 2008 No 10, IMADA, SDU.
Contributions to the Theory of Colourings, Graph Minors, and Independent Sets PhD thesis, November, 2010. (Second Edition, August, 2011)
A χ-binding function for the class of {3K_{1}, K_{1} ∪ K_{4}}-free graphs, manuscript, April, 2011. (Conjecture 2.4 on independent sets and matchings in triangle-free subcubic graphs was subsequently proved to be true by Löwenstein, Henning, and Rautenbach in their paper Independent sets and matchings in subcubic graphs.)
On graphs double-critical with respect to the colouring number, with Matthias Kriesell, arXiv:1108.1036, August, 2011, submitted.
Hadwiger's Conjecture for inflations of 3-chromatic graphs, with Carl Johan Casselgren, IML-1314s-28, September, 2014. To appear in European Journal of Combinatorics.
Inflations of anti-cycles and Hadwiger's Conjecture, with Mike Plummer and Bjarne Toft, accepted for publication, 2015.
Inflations of graphs, ongoing project.
Concerning the Double-Critical Hadwiger Conjecture: Boris Albar and Daniel Gonçalves (On triangles in K_r-minor free graphs) (arXiv:1304.5468, 2013) prove that every double-critical 8-chromatic graph contains a K_8-minor. (Thus, finding the edge I was missing in [Electron. J. Combin., 18(1): Research Paper 80, 2011] ☺ )
Computational results (obtained using CPLEX, Sage and/or geng):
25.08.2012: A list of all small squco graphs
20.09.2012: The Strong Chromatic Index Conjecture holds for all simple graphs on at most 10 vertices.
24.09.2012: The Double-Critical Graph Conjecture holds for all graphs on at most 12 vertices. (note)
07.10.2012: A list of all small double-col-critical graphs with colouring number 6
30.12.2012: The Bollobás-Eldridge-Catlin Conjecture holds for all graphs on at most 9 vertices. (The BEC-conjecture at Open problems garden.)
13.01.2013: The Strong Chromatic Index Conjecture holds for all simple graphs on at most 11 vertices. (Thanks to M. Chiarandini and N. Cohen for help on CPLEX.)
08.02.2013: Reed's omega, delta, and chi conjecture holds for all graphs on at most 12 vertices.
26.02.2013: Reed's omega, delta, and chi conjecture for triangle-free graphs holds for all graphs on at most 13 vertices.
03.03.2013: Concerning Melnikov's valency-variety problem: the proposed lower bound on the chromatic number holds for all graphs on at most 10 vertices.
15.03.2013: The Kostochka-Yu conjecture holds for all graphs on at most 8 vertices.
18.08.2013: The Kostochka-Yu conjecture holds for all graphs on at most 9 vertices.
31.05.2015: Every bipartite graph G on at most 12 vertices has a complete minor of order at least col(G) [degeneracy+1] (cf. Problem 6.6.1 in my PhD-thesis, 2nd ed.).
07.06.2015: Every bipartite graph G on at most 13 vertices has a complete minor of order at least col(G).
20.06.2015: Every bipartite graph G on at most 14 vertices has a complete minor of order at least col(G).
08.07.2015: Hajos' Conjecture holds for every graph on at most 10 vertices. (Smallest known counterexample has 13 vertices.)
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