000			01953n a2200301#a 4500
001			40126
003			P5A
005			20230123132002.0
007			cr cuuuuuauuuu
008			210830s2021 bl por d
035			_aocm51338542
040			_aP5A _cP5A
090			_atimpa
100	1		_aSpier, Thomas Jung _99386
245	1	0	_aGraph Continued Fractions/ _cThomás Jung Spier.
246	1		_aFrações Contínuas de Grafos
260			_aRio de Janeiro: _bIMPA, _c2021.
300			_avideo online
500			_aDefesa de Tese.
500			_aBanca examinadora: Carlos Gustavo Moreira - Orientador - IMPA Dimitar Dimitrov - Coorientador - UNESP Rob Morris - IMPA Nicolau Saldanha - PUC-Rio Gabriel Coutinho - UFMG Eduardo Tengan - UFSC
505	1		_aAbstract: This thesis studies a connection between matching polynomials and continued fractions. For the matching polynomials: we prove a refinement of a theorem by Ku and Wong, which extends the classical Gallai-Edmonds decomposition; we present a generalization of Sturm's classical theorem about the number of zeros of a real polynomial in an interval; we characterize the number of distinct zeros in terms of the dimension of a vector space generated by a family of matching polynomials; we prove an upper bound on the number of paths that start at some vertex of a graph. We also present simple formulas for means of continued fractions that are useful in the classical theory of the Pell equation .
650	0	4	_aMatematica. _2larpcal _919899
697			_aTeses do IMPA _924311
700	1		_aMoreira, Carlos Gustavo T. de A. _u(IMPA) _eorientador _912783
711	2		_aDefesa de Tese _910070
856	4		_zVIDEO _uhttps://bit.ly/3kvMNhC
942			_2impa _cVIDEO
999			_aGRAPH Continued Fractions. Thomás Jung Spier. Rio de Janeiro: IMPA, 2021. video online. Disponível em: https://bit.ly/3kvMNhC. Acesso em: 30 ago. 2021. _c38767 _d38767