A note on the real part of complex chromatic roots

Brown, Jason I.; Erey, Aysel

doi:10.1016/j.disc.2014.04.007

Cited by 3 publications

(3 citation statements)

References 13 publications

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“…Moreover, studying σ‐polynomials is useful to find chromatically equivalent or chromatically unique graph families [, ]. Recently, in , the authors obtained upper bounds for the real parts of the roots of chromatic polynomials for graphs with large chromatic number by investigating the σ‐polynomials of such graphs.…”

Section: Introductionmentioning

confidence: 99%

On the Roots of σ‐Polynomials

Brown

Erey

2015

Journal of Graph Theory

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Given a graph G of order n, the σ‐polynomial of G is the generating function σ(G,x)=∑aixi where ai is the number of partitions of the vertex set of G into i nonempty independent sets. Such polynomials arise in a natural way from chromatic polynomials. Brenti (Trans Am Math Soc 332 (1992), 729–756) proved that σ‐polynomials of graphs with chromatic number at least n−2 had all real roots, and conjectured the same held for chromatic number n−3. We affirm this conjecture.

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Section: Introductionmentioning

confidence: 99%

On the Roots of σ‐Polynomials

Brown

Erey

2015

Journal of Graph Theory

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“…Moreover, studying σ-polynomials is useful to find chromatically equivalent or chromatically unique graph families [15,20]. Recently, in [3], the authors obtained upper bounds for the real parts of the roots of chromatic polynomials for graphs with large chromatic number by investigating the σ-polynomials of such graphs.…”

Section: Introductionmentioning

confidence: 99%

On the roots of $σ$-polynomials

Brown,

Erey

2013

Preprint

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Given a graph G of order n, the σ-polynomial of G is the generating function σ(G, x) = a i x i where a i is the number of partitions of the vertex set of G into i nonempty independent sets. Such polynomials arise in a natural way from chromatic polynomials. Brenti [1] proved that σ-polynomials of graphs with chromatic number at least n − 2 had all real roots, and conjectured the same held for chromatic number n − 3. We affirm this conjecture.

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“…100 For our purposes, what is interesting is that CCD relied on the CRPD to argue that the duty to accommodate included a duty to consult. 101 In Brown, the underlying facts were challenging because many observers might see the claim as frivolous, especially as Canadian cities are replete with so many accessibility barriers. However, it may be that such arguments would be successful in a stronger case and the CRPD could effectively bolster a rethinking of what accessibility in the built environment means.…”

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confidence: 99%

The United Nations Convention on the Rights of Persons With Disabilities in Canadian and American Jurisprudence

Malhotra

2015

WYAJ

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In this paper, I explore the still evolving jurisprudence with respect to the Convention on the Rights of Persons with Disabilities [CRPD] in Canada and the United States. I argue that the Canadian disability rights movement has always been open to insights from international law. Although the 1990 passage of the landmark Americans with Disabilities Act [ADA] has had an impact internationally as other countries enact similar legislation, the CRPD, which the United States Senate has yet to ratify, has played a marginal role to date in American courts. It remains to be seen if a more robust judicial dialogue can be fostered between the CRPD and domestic courts in both countries. Dans le présent document, j’explore la jurisprudence toujours en évolution au sujet de l’application de la Convention relative aux droits des personnes handicapées [CDPH] au Canada et aux États‑Unis. Je soutiens que le mouvement canadien de défense des droits des handicapés a toujours été ouvert aux points de vue émanant du droit international. Bien que l’adoption, en 1990, de la loi clé intitulée Americans with Disabilities Act [ADA] ait eu des répercussions à l’échelle internationale, puisque d’autres pays ont adopté des lois similaires, la CDPH, que le Sénat américain n’a pas encore ratifiée, a joué un rôle marginal jusqu’à maintenant devant les tribunaux américains. Il reste à déterminer s’il est possible de promouvoir un dialogue judiciaire plus vigoureux entre les organes qui appliquent la CDPH et les tribunaux nationaux des deux pays.

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A note on the real part of complex chromatic roots

Cited by 3 publications

References 13 publications

On the Roots of σ‐Polynomials

On the Roots of σ‐Polynomials

On the roots of $σ$-polynomials

The United Nations Convention on the Rights of Persons With Disabilities in Canadian and American Jurisprudence

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