Polynomial graph invariants and the KP hierarchy
نویسندگان
چکیده
منابع مشابه
Graph invariants, homomorphisms, and the Tutte polynomial
There are various ways to define the chromatic polynomial P (G; z) of a graph G. Perhaps the first that springs to mind is to define it to be the graph invariant P (G; k) with the property that when k is a positive integer P (G; k) is the number of colourings of the vertices of G with k or fewer colours such that adjacent vertices receive different colours. One then has to prove that P (G; k) i...
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In [1], Airault, McKean and Moser observed that the motion of poles of a rational solution to the K-dV or Boussinesq equation obeys the Calogero-Moser dynamical system [2, 3, 4] with an extra condition on the configuration of poles. In [8], Krichever observed that the motion of poles of a solution to the KP equation which is rational in t1 obeys the Calogero-Moser dynamical system. In this note...
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The number of homomorphisms hom(G,Kk) from a graph G to the complete graph Kk is the value of the chromatic polynomial of G at a positive integer k. This motivates the following (cf. [3]): Definition 1 A sequence of graphs (Hk), k = (k1, . . . , kh) ∈ N , is strongly polynomial if for every graph G there is a polynomial p(G; x1, . . . , xh) such that hom(G,Hk) = p(G; k1, . . . , kh) for every k...
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ژورنال
عنوان ژورنال: Selecta Mathematica
سال: 2020
ISSN: 1022-1824,1420-9020
DOI: 10.1007/s00029-020-00562-w