R. Arratia, B. Bollobas, and G.B. Sorkin. The interlace polynomial: A new graph polynomial. IBM Research Report, RC 21813 (98165), 31 July 2000. Home/Search Document Details and Download
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Farrell Polynomials on Graphs of Bounded Tree Width - Makowsky, Mariño (2000) (Correct)
....and all the polynomials which are substitution instances thereof, especially Kauffman brackets and other knot polynomials viewed as graph polynomials. BR99] This was shown in [Mak01,Mak00] This also includes Martin polynomials and the interlace polynomial, if restricted to link like graphs, cf. [EM98,ABS]. ii) Farrell s F polynomials for F covers, cf. Far79b] with F a finite set of graphs. This includes both the matching defect polynomial, the matching generating polynomial, cf. LP86] and their generalizations, cf. God81,God93,Far79a] the various rook polynomials of Riordan, Rio58] and ....
....The bounded frame polynomials. Our method does not apply to the following: The Martin polynomials, which are Farrell polynomials for edge disjoint covers. However, for graphs representing link diagrams (e.g. eulerian and regular of degree 4) they can be obtained from the Kauffman bracket, cf. [ABS]. Based on recent work on Martin polynomials on arbitrary graphs in [EM98] we conjecture: Conjecture 1. On graphs of tree width at most k the Martin polynomials can be computed in polynomial time. However, the proof we have to use some new ideas. The permanent polynomial, because the permanent ....
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R. Arratia, B. Bollobas, and G.B. Sorkin. The interlace polynomial: A new graph polynomial. IBM Research Report, RC 21813 (98165), 31 July 2000.
The Interlace Polynomial: A New Graph Polynomial - Arratia, Bollobas, Sorkin (2000) (1 citation) Self-citation (Arratia Sorkin) (Correct)
....= Gamma1) n Gamma1 a(D) 2 2 a(D) 1 ( Gamma1) n Gamma1 a(D) 1 2 a(D) Gamma1) n a(D) 1 2 a(D) completing the proof. Corollary 29. Let H be a circle graph. Then q H ( Gamma1) Gamma1) jHj 1 ( Gamma2) k for some non negative integer k. This led us to conjecture in [ABS00] that for all undirected graphs G, not just circle graphs, q(G; Gamma1) Gamma1) jGj ( Gamma2) k for some value k; this has recently been proved in [BBCP] It has implications that may be at least as interesting. If ab is an edge of H and G = H Gamma a, then q(H; Gamma1) q(G; Gamma1) ....
Richard Arratia, B'ela Bollob'as, and Gregory B. Sorkin, The interlace polynomial: A new graph polynomial, Proceedings of the Eleventh Annual ACM--SIAM Symposium on Discrete Algorithms (San Francisco, CA), January 2000, pp. 237--245.
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