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Preface: Special issue on the Tutte polynomial
JID:YAAMA
AID:1798 /EDI
[m1L; v1.223; Prn:6/10/2017; 9:46] P.1 (1-2) Advances in Applied Mathematics ••• (••••) •••–•••
Contents lists available at ScienceDirect
Advances in Applied Mathematics www.elsevier.com/locate/yaama
Preface: Special issue on the Tutte polynomial This special issue originated in the Workshop on the Tutte Polynomial, held at Royal Holloway University of London, July 11 to 14, 2015. It was supported by EPSRC (grant EP/M023680/1). Some but not all of the papers were presented at the workshop. The six papers in this special issue give a cross-section of current work on graph and matroid invariants related to the Tutte polynomial. The paper of Clark Butler gives an expansion of the Krushkal polynomial, a 4-variable polynomial defined on a graph embedded on a surface, by activities of quasi-trees of ribbon graphs. Spencer Backman shows that several evaluations of the Tutte polynomial count partial orientations of graphs with various properties. An extensive survey on orientations and the Tutte polynomial, by Emeric Gioan and Michel Las Vergnas, was planned for this issue but was delayed. We expect this paper to appear in this journal in the near future. The paper of A. Goodall, M. Hermann, T. Kotek, J.A. Makowsky, and S.D. Noble is about the computational complexity of evaluating polynomials defined on graphs similar to the chromatic polynomial, in that they give the number of colorings satisfying a variety of conditions. Kolja Knauer, Leonardo Martinez-Sandoval, and Jorge Luis Ramirez Alfonsin settle the Merino–Welsh conjecture for lattice path matroids in the form T (M ; 2, 0)T (M ; 0, 2) ≥ 43 T (M ; 1, 1)2 . Considering the transition polynomial of a multimatroid, Robert Brijder gives a unifying account of interlace, Tutte–Martin, and other polynomials. A new invariant for matroids is the G-invariant defined by Harm Derksen. This invariant is not a polynomial but includes the Tutte polynomial as a specialization. In their paper, Joseph Bonin and Joseph Kung show that many of the results on Tutte polynomials, particularly those on matroid constructions, have close analogs for the G-invariant.
https://doi.org/10.1016/j.aam.2017.09.005 0196-8858/© 2017 Elsevier Inc. All rights reserved.
JID:YAAMA 2
AID:1798 /EDI
[m1L; v1.223; Prn:6/10/2017; 9:46] P.2 (1-2) Preface: Special issue on the Tutte polynomial
Guest Editors Joanna A. Ellis Monaghan Saint Michael’s College, Colchester, VT 05439, USA E-mail address: [email protected] Joseph P.S. Kung Department of Mathematics, University of North Texas, Denton, TX 76203, USA E-mail address: [email protected] Iain Moffatt Department of Mathematics, Royal Holloway University of London, Egham, Surrey TW20 0EX, United Kingdom E-mail address: iain.moff[email protected] Available online xxxx
AID:1798 /EDI
[m1L; v1.223; Prn:6/10/2017; 9:46] P.1 (1-2) Advances in Applied Mathematics ••• (••••) •••–•••
Contents lists available at ScienceDirect
Advances in Applied Mathematics www.elsevier.com/locate/yaama
Preface: Special issue on the Tutte polynomial This special issue originated in the Workshop on the Tutte Polynomial, held at Royal Holloway University of London, July 11 to 14, 2015. It was supported by EPSRC (grant EP/M023680/1). Some but not all of the papers were presented at the workshop. The six papers in this special issue give a cross-section of current work on graph and matroid invariants related to the Tutte polynomial. The paper of Clark Butler gives an expansion of the Krushkal polynomial, a 4-variable polynomial defined on a graph embedded on a surface, by activities of quasi-trees of ribbon graphs. Spencer Backman shows that several evaluations of the Tutte polynomial count partial orientations of graphs with various properties. An extensive survey on orientations and the Tutte polynomial, by Emeric Gioan and Michel Las Vergnas, was planned for this issue but was delayed. We expect this paper to appear in this journal in the near future. The paper of A. Goodall, M. Hermann, T. Kotek, J.A. Makowsky, and S.D. Noble is about the computational complexity of evaluating polynomials defined on graphs similar to the chromatic polynomial, in that they give the number of colorings satisfying a variety of conditions. Kolja Knauer, Leonardo Martinez-Sandoval, and Jorge Luis Ramirez Alfonsin settle the Merino–Welsh conjecture for lattice path matroids in the form T (M ; 2, 0)T (M ; 0, 2) ≥ 43 T (M ; 1, 1)2 . Considering the transition polynomial of a multimatroid, Robert Brijder gives a unifying account of interlace, Tutte–Martin, and other polynomials. A new invariant for matroids is the G-invariant defined by Harm Derksen. This invariant is not a polynomial but includes the Tutte polynomial as a specialization. In their paper, Joseph Bonin and Joseph Kung show that many of the results on Tutte polynomials, particularly those on matroid constructions, have close analogs for the G-invariant.
https://doi.org/10.1016/j.aam.2017.09.005 0196-8858/© 2017 Elsevier Inc. All rights reserved.
JID:YAAMA 2
AID:1798 /EDI
[m1L; v1.223; Prn:6/10/2017; 9:46] P.2 (1-2) Preface: Special issue on the Tutte polynomial
Guest Editors Joanna A. Ellis Monaghan Saint Michael’s College, Colchester, VT 05439, USA E-mail address: [email protected] Joseph P.S. Kung Department of Mathematics, University of North Texas, Denton, TX 76203, USA E-mail address: [email protected] Iain Moffatt Department of Mathematics, Royal Holloway University of London, Egham, Surrey TW20 0EX, United Kingdom E-mail address: iain.moff[email protected] Available online xxxx