A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2017; you can also visit the original URL.
The file type is `application/pdf`

.

## Filters

##
###
Algorithms
[chapter]

2011
*
Graph Coloring Problems
*

Jaeger's Circular

doi:10.1002/9781118032497.ch10
fatcat:374tktuvgvekni4fnz3dgbytjm
*Flow*Conjecture Berge's Strong Path Partition Conjecture Berge's*Directed*Path-Conjecture Minimal Orientations of Critical*Graphs*Alon-Tarsi Orientations*and**Chromatic*Number Bibliography ...*Polynomials*14.1 14.2 14.3 14.4 14.5 14.6 14.7 14.8 Coefficients of*Chromatic**Polynomials*Characterization of*Chromatic**Polynomials**Chromatic*Uniqueness*Chromatic*Equivalence Zeros of*Chromatic*...##
###
The Chromatic Polynomial of a Digraph
[article]

2022
*
arXiv
*
pre-print

This decomposition will confirm the equality of our

arXiv:1911.09547v3
fatcat:jhmi3sxkjrhqtcgr6mtufluvx4
*chromatic**polynomial*of a digraph*and*the*chromatic**polynomial*of the underlying undirected*graph*in the case of symmetric digraphs. ... Furthermore we will decompose our NL-coflow*polynomial*, which becomes the*chromatic**polynomial*of a digraph by multiplication with the number of colors to the number of components, examining the special ... Probably, the*chromatic**polynomial*of a*graph*is better known than the*flow**polynomial*. ...##
###
Page 5776 of Mathematical Reviews Vol. , Issue 95j
[page]

1995
*
Mathematical Reviews
*

W. (4-LNDHB; Egham) Reciprocity

*and**polynomial*properties*for*even*flows**and*potentials on*directed**graphs*. (English summary) Combin. Probab. Comput. 3 (1994), no. 1, 1-11. ... 95}:05097 umbral*chromatic**polynomials*. {*For*the entire collection see MR 94i:05001.} ...##
###
On chromatic and flow polynomial unique graphs

2008
*
Discrete Applied Mathematics
*

It is known that the

doi:10.1016/j.dam.2007.10.010
fatcat:6fxjxx7owfh73orj6su54oih7m
*chromatic**polynomial**and**flow**polynomial*of a*graph*are two important evaluations of its Tutte*polynomial*, both of which contain much information of the*graph*. ... Finally, we show that several classes of*graphs*, ladders, Möbius ladders*and*squares of n-cycle are determined by their*chromatic**polynomials**and**flow**polynomials*together. ... The second author's research was done while he was visiting the Center*for*Combinatorics at Nankai University. He is very grateful*for*the hospitality provided by the University. ...##
###
Page 7177 of Mathematical Reviews Vol. , Issue 95m
[page]

1995
*
Mathematical Reviews
*

*For*odd A, the values

*for*even f,

*and*odd # separately, also have

*polynomial*dependence on f

*and*are

*directing*dependent. ... A different

*polynomial*may be required

*for*different

*directings*of the same undirected

*graph*

*and*

*for*each odd-PD problem there is an equivalent even- PD problem on the reversed

*graph*. ...

##
###
Binomial Inequalities for Chromatic, Flow, and Tension Polynomials
[article]

2021
*
arXiv
*
pre-print

*For*example, we show that χ^*_ j ≤χ^*_ d-j,

*for*0 ≤ j ≤ d / 2. Similar results hold

*for*

*flow*

*and*tension

*polynomials*enumerating either modular or integral nowhere-zero

*flows*/tensions of a

*graph*. ... A famous

*and*wide-open problem, going back to at least the early 1970's, concerns the classification of

*chromatic*

*polynomials*of

*graphs*. ... As is well known,

*for*a given

*graph*G, the number χ G (n) of proper colorings of G using n colors evaluates to a

*polynomial*in n,

*and*so a natural question is: which

*polynomials*are

*chromatic*? ...

##
###
Graph polynomials and their applications I: The Tutte polynomial
[article]

2008
*
arXiv
*
pre-print

These include several ways in which a

arXiv:0803.3079v2
fatcat:gi6d5vkh3rdfjendtjipx3y73u
*graph**polynomial*may be defined*and*methods*for*extracting combinatorial information*and*algebraic properties from a*graph**polynomial*. ... We explore some of the Tutte polynomial's many properties*and*applications*and*we use the Tutte*polynomial*to showcase a variety of principles*and*techniques*for**graph**polynomials*in general. ... Jackson [Jac03] surveys zeros of both*chromatic**and*the*flow**polynomials*. ...##
###
Tutte relations, TQFT, and planarity of cubic graphs
[article]

2015
*
arXiv
*
pre-print

A version of the Tutte linear relation

arXiv:1512.07339v1
fatcat:2ciouelmjncp5b7gee4ndlbnza
*for*the*flow**polynomial*at (3-√(5))/2 is shown to give a planarity criterion*for*3-connected cubic*graphs*. ... A conjecture is formulated that the golden identity*for*the*flow**polynomial*characterizes planarity of cubic*graphs*as well. ... The authors would like to thank the IHES*for*hospitality*and*support (NSF grant 1002477). Ian Agol was partially supported by NSF grant DMS-1406301,*and*by a Simons Investigator grant. ...##
###
Page 1336 of Mathematical Reviews Vol. , Issue 85d
[page]

1985
*
Mathematical Reviews
*

The

*chromatic**polynomials*of connected*graphs*with k edges*and*k — 2 vertices all of degree at least 2 are determined*for*k > 6. ... problem to a class of*graphs*whose edges can be covered by three cobases of the*flow*matroid,*and*the construction of the required*flow**for*this class. ...##
###
Structure of the flow and Yamada polynomials of cubic graphs
[article]

2018
*
arXiv
*
pre-print

The golden identity

arXiv:1801.00502v1
fatcat:x7xdh2brfbfghlfd5zsfrgwcbi
*for*the*flow**polynomial*is conjectured to characterize planarity of cubic*graphs*,*and*we prove this conjecture*for*a certain infinite family of non-planar*graphs*. ... An application is given to the structure of the*flow**polynomial*of cubic*graphs*at zero. ... We would like to thank Gordon Royle*for*many discussions,*and*also*for*sharing with us numerical data on*graph**polynomials*. We also thank Kyle Miller*for*helpful comments. V. ...##
###
Page 1570 of Mathematical Reviews Vol. 56, Issue 5
[page]

1978
*
Mathematical Reviews
*

Let G be a

*graph**and*P(A, G) its*chromatic**polynomial*. ...*For**directed**graphs*without double-entry cycles (*flow*returns tu predecessor points only) a method is given to compute a minimal blocking point set. ...##
###
Graphs whose flow polynomials have only integral roots
[article]

2009
*
arXiv
*
pre-print

We show if the

arXiv:0908.0181v2
fatcat:ctooxct4pfh4zlp4codahacnoq
*flow**polynomial*of a bridgeless*graph*G has only integral roots, then G is the dual*graph*to a planar chordal*graph*. ... We also show that*for*3-connected cubic*graphs*, the same conclusion holds under the weaker hypothesis that it has only real*flow*roots. ... See,*for*example, [11] . In the context of matroids,*chromatic**and**flow**polynomials*would seem to be very special cases. ...##
###
Graphs whose flow polynomials have only integral roots

2011
*
European journal of combinatorics (Print)
*

We show if the

doi:10.1016/j.ejc.2011.01.010
fatcat:pxsdxmaxlfcsvmmjmplozrshwa
*flow**polynomial*of a bridgeless*graph*G has only integral roots, then G is the dual*graph*to a planar chordal*graph*. ... We also show that*for*3-connected cubic*graphs*, the same conclusion holds under the weaker hypothesis that it has only real*flow*roots. ... It is a little harder to give a*direct*counting argument analogous to the*chromatic**polynomial*case, but this can be done by considering*flows*with values in the*direct*product Z m 2 of m copies of the ...##
###
Graph Polynomials: Towards a Comparative Theory (Dagstuhl Seminar 16241)

2016
*
Dagstuhl Reports
*

The area of

doi:10.4230/dagrep.6.6.26
dblp:journals/dagstuhl-reports/Ellis-MonaghanG16
fatcat:6mhgqibwa5av7dxeye2y6wgytm
*graph**polynomials*has become in recent years incredibly active, with new applications*and*new*graph**polynomials*being discovered each year. ... This report documents the program*and*the outcomes of Dagstuhl Seminar 16241 "*Graph**Polynomials*: Towards a Comparative Theory". ... Tutte constructed his dichromate as a bivariate generalization of the*chromatic**polynomial**and**flow**polynomial*. The Tutte*polynomial*extends from*graphs*to matroids more generally. ...##
###
Computing Tutte Polynomials

2010
*
ACM Transactions on Mathematical Software
*

It contains several other

doi:10.1145/1824801.1824802
fatcat:hvug6yat6ndm3dphurbbz32yne
*polynomial*invariants, such as the*chromatic**polynomial**and**flow**polynomial*as partial evaluations,*and*various numerical invariants such as the number of spanning trees as complete ... The Tutte*polynomial*of a*graph*, also known as the partition function of the q-state Potts model, is a 2-variable*polynomial**graph*invariant of considerable importance in both combinatorics*and*statistical ... We wish to thank the Isaac Newton Institute*for*Mathematical Sciences, University of Cambridge,*for*generous support during the programme on Combinatorics*and*Statistical Mechanics (January -June 2008) ...
« Previous

*Showing results 1 — 15 out of 2,149 results*