Results 31 to 40 of about 495 (157)
G-Tutte Polynomials and Abelian Lie Group Arrangements [PDF]
, 2021 For a list A of elements in a finitely generated abelian group Gamma and an abelian group G, we introduce and study an associated G-Tutte polynomial, defined by counting the number of homomorphisms from associated finite abelian groups to G.
Tan Nhat Tran +2 more
core +1 more source
, 2022 18 pages, 6 figures. This is a draft of a chapter for the Handbook on the Tutte Polynomial. Comments are welcome!
openaire +2 more sources
Tutte polynomials for directed graphs
Journal of Combinatorial Theory, Series B, 2020 The Tutte polynomial is a fundamental invariant of graphs. In this article, we define and study a generalization of the Tutte polynomial for directed graphs, that we name B-polynomial. The B-polynomial has three variables, but when specialized to the case of graphs (that is, digraphs where arcs come in pairs with opposite directions), one of the ...
Jordan Awan, Olivier Bernardi
openaire +4 more sources
An inequality for Tutte polynomials [PDF]
Combinatorica, 2010 The Tutte polynomial of the graph \(G=(V,E)\) can be defined by the closed formula \[ TG(x, y) =\sum_{A\subseteq E} (x - 1)^{r(E)-r(A)}(y - 1)^{| A| -r(A)} \] where \(r(A)=| V | -\omega (V,A)\), and \(\omega(V,A)\) denotes the number of components in the graph \((V,A)\). The author proves that, for a graph \(G\) without loops or bridges and \(a\), \(b\)
openaire +2 more sources
The Arithmetic Tutte polynomial of two matrices associated to Trees
Special Matrices, 2018 Arithmetic matroids arising from a list A of integral vectors in Zn are of recent interest and the arithmetic Tutte polynomial MA(x, y) of A is a fundamental invariant with deep connections to several areas. In this work, we consider two lists of vectors
Bapat R. B. +1 more
doaj +1 more source
Tutte Polynomial of Multi-Bridge Graphs [PDF]
Computer Science Journal of Moldova, 2013 In this paper, using a well-known recursion for computing the Tutte polynomial of any graph, we found explicit formulae for the Tutte polynomials of any multi-bridge graph and some $2-$tree graphs.
Julian A. Allagan
doaj
Evaluating the Tutte Polynomial for Graphs of Bounded Tree-Width
, 1998 It is known that evaluating the Tutte polynomial, $T(G; x, y)$, of a graph, $G$, is $\#$P-hard at all but eight specific points and one specific curve of the $(x, y)$-plane.
Noble, Steven, S. D. Noble, Noble, S D
core +1 more source
An Interpretation for the Tutte Polynomial
European Journal of Combinatorics, 1999 For a matroid \(M\) which is representable over the rational numbers the author gives a new interpretation of the Tutte polynomial \(T_M(x,y)\) associated to \(M\). The Tutte polynomial \(T_M(x,y)\) of a matroid \(M\) is a or may be the fundamental invariant of \(M\). After its definition by \textit{W. T. Tutte} in 1947 [Proc. Camb. Philos. Soc. 43, 26-
openaire +1 more source
Tutte polynomials computable in polynomial time
Discrete Mathematics, 1992 Determining the Tutte polynomial of a matroid at a fixed point \(P\) of the plane is known to be \(\# P\)-hard unless \(P\) lies on a certain hyperbola or is one of 8 special points (\textit{F. Jaeger}, \textit{D. L. Vertigan} and the second author [Math. Proc. Camb. Philos. Soc. 108, No. 1, 35-53 (1990; Zbl 0747.57006)]). The authors show that for any
James G. Oxley, Dominic J. A. Welsh
openaire +2 more sources
The equivalence of two graph polynomials and a symmetric function
, 2009 The U-polynomial, the polychromate and the symmetric function generalization of the Tutte polynomial due to Stanley are known to be equivalent in the sense that the coefficients of any one of them can be obtained as a function of the coefficients of any ...
Noble, SD +5 more
core +1 more source