A note on counting flows in signed graphs

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F19%3A10405098" target="_blank" >RIV/00216208:11320/19:10405098 - isvavai.cz</a>
Result on the web
<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=FrjiY9Tbnv" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=FrjiY9Tbnv</a>
DOI - Digital Object Identifier
—

Result language
angličtina
Original language name
A note on counting flows in signed graphs
Original language description
Tutte initiated the study of nowhere-zero flows and proved the following fundamental theorem: For every graph G there is a polynomial f so that for every abelian group Gamma of order n, the number of nowhere-zero Gamma-flows in G is f (n). For signed graphs (which have bidirected orientations), the situation is more subtle. For a finite group Gamma, let epsilon(2)(Gamma) be the largest integer d so that Gamma has a subgroup isomorphic to Z(2)(d). We prove that for every signed graph G and d >= 0 there is a polynomial f(d) so that f(d) (n) is the number of nowhere-zero Gamma-flows in G for every abelian group Gamma with epsilon(2)(Gamma) = d and vertical bar Gamma vertical bar = 2(d)n. Beck and Zaslaysky [JCTB 2006] had previously established the special case of this result when d = 0 (i.e., when Gamma has odd order).
Czech name
—
Czech description
—

Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
OECD FORD branch
10101 - Pure mathematics

Project
Result was created during the realization of more than one project. More information in the Projects tab.
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2019
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Similar results(10)