Results 81 to 90 of about 2,394 (219)
An attempt to classify bipartite graphs by their chromatic Polynomial. [PDF]
, 2009 For the purpose of tackling the four-colour problem, Birkhoff (1912) introduced the chromatic polynomial of a map, denoted by P(M,A), which is a number of proper Acolouring of a map M.
Hasni, Roslan
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Chromatic Polynomials of Oriented Graphs
The Electronic Journal of Combinatorics, 2019 The oriented chromatic polynomial of a oriented graph outputs the number of oriented $k$-colourings for any input $k$. We fully classify those oriented graphs for which the oriented graph has the same chromatic polynomial as the underlying simple graph, closing an open problem posed by Sopena.
Danielle Cox, Christopher Duffy 0001
openaire +4 more sources
On Oriented Colourings of Graphs on Surfaces
Journal of Graph Theory, Volume 112, Issue 4, Page 357-369, August 2026.ABSTRACT For an oriented graph G, the least number of colours required to oriented colour G is called the oriented chromatic number of G and denoted χ o ( G ). For a non‐negative integer g let χ o ( g ) be the least integer such that χ o ( G ) ≤ χ o ( g ) for every oriented graph G with Euler genus at most g.
Alexander Clow
wiley +1 more source
Food Science &Nutrition, Volume 14, Issue 7, July 2026.This study evaluated the efficacy of an ultrasound pre‐treatment applied to a complex cereal–milk infant formula prior to conventional spray drying to mitigate inherent stickiness and yield challenges. Acoustic cavitation (30–90 s) significantly reduced suspension viscosity and improved atomization efficiency, elevating powder recovery yield from 12 ...
Yamen Barakat +2 more
wiley +1 more source
Explicit formulas for chromatic polynomials of some series-parallel graphs
Учёные записки Казанского университета: Серия Физико-математические науки, 2018 The main goal of our paper is to present explicit formulas for chromatic polynomials of some planar series-parallel graphs (sp-graphs). The necklace-graph considered in this paper is the simplest non-trivial sp-graph.
E.Yu. Lerner, S.A. Mukhamedjanova
doaj
Treewidth Versus Clique Number. V. Further Connections With Tree‐Independence Number
Journal of Graph Theory, Volume 112, Issue 3, Page 337-351, July 2026.ABSTRACT We continue the study of ( tw , ω )‐bounded graph classes, that is, hereditary graph classes in which large treewidth is witnessed by the presence of a large clique, and the relation of this property to boundedness of the tree‐independence number, a graph parameter introduced independently by Yolov in 2018 and by Dallard, Milanič, and Štorgel ...
Claire Hilaire +2 more
wiley +1 more source
Bounds on the complex zeros of (Di)Chromatic polynomials and Potts-model partition functions
, 2001 We show that there exist universal constants C(r) such that, for all loopless graphs G of maximum degree less than or equal to r, the zeros (real or complex) of the chromatic polynomial P-G(q) lie in the disc \q\ 7.963907r.
Sokal, AD
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A Note on a Broken-Cycle Theorem for Hypergraphs
Discussiones Mathematicae Graph Theory, 2014 Whitney’s Broken-cycle Theorem states the chromatic polynomial of a graph as a sum over special edge subsets.
Trinks Martin
doaj +1 more source
Food Science &Nutrition, Volume 14, Issue 6, June 2026.This review elucidates the mechanistic pathways governing color and texture degradation in frozen tropical vegetables, emphasizing pigment oxidation, enzymatic softening, and ice crystal‐induced structural damage. It integrates kinetic, Arrhenius, RSM, and machine‐learning models with advanced preservation strategies to optimize freezing processes ...
Muhammad Muntasir Mahmud +4 more
wiley +1 more source
Chromatic roots are dense in the whole complex plane
, 2004 I show that the zeros of the chromatic polynomials P-G(q) for the generalized theta graphs Theta((s.p)) are taken together, dense in the whole complex plane with the possible exception of the disc \q - l\ < l.
Sokal, AD
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