scholarly journals A zero-free interval for chromatic polynomials of graphs with 3-leaf spanning trees

2016 ◽  
Vol 339 (11) ◽  
pp. 2706-2714 ◽  
Author(s):  
Thomas Perrett
Keyword(s):  
Spanning Trees ◽  
Chromatic Polynomials ◽  
Free Interval

scholarly journals A zero-free interval for chromatic polynomials

1992 ◽  
Vol 101 (1-3) ◽  
pp. 333-341 ◽  
Author(s):  
D.R. Woodall
Keyword(s):  
Chromatic Polynomials ◽  
Free Interval

A Contribution to the Theory of Chromatic Polynomials

1954 ◽  
Vol 6 ◽  
pp. 80-91 ◽  
Author(s):  
W. T. Tutte
Keyword(s):  
Connected Graph ◽  
Planar Graphs ◽  
Spanning Trees ◽  
Chromatic Polynomials ◽  
Colour Problem ◽  
General Graphs

SummaryTwo polynomials θ(G, n) and ϕ(G, n) connected with the colourings of a graph G or of associated maps are discussed. A result believed to be new is proved for the lesser-known polynomial ϕ(G, n). Attention is called to some unsolved problems concerning ϕ(G, n) which are natural generalizations of the Four Colour Problem from planar graphs to general graphs. A polynomial χ(G, x, y) in two variables x and y, which can be regarded as generalizing both θ(G, n) and ϕ(G, n) is studied. For a connected graph χ(G, x, y) is defined in terms of the “spanning” trees of G (which include every vertex) and in terms of a fixed enumeration of the edges.

A Zero-Free Interval for Chromatic Polynomials of Graphs

1993 ◽  
Vol 2 (3) ◽  
pp. 325-336 ◽  
Author(s):  
Bill Jackson
Keyword(s):  
Chromatic Polynomial ◽  
Chromatic Polynomials ◽  
Free Interval

LetGbe a graph andP(G, t) be the chromatic polynomial ofG. It is known thatP(G, t) has no zeros in the intervals (−∞, 0) and (0, 1). We shall show thatP(G, t) has no zeros in (1, 32/27]. In addition, we shall construct graphs whose chromatic polynomials have zeros arbitrarily close to 32/27.

Hepatitis-Free Interval After Clotting Factor Therapy in First Infused Haemophiliacs

1986 ◽  
Vol 56 (03) ◽  
pp. 268-270 ◽  
Author(s):  
M Morfini ◽  
D Rafanelli ◽  
G Longo ◽  
A Messori ◽  
P Rossi Ferrini
Keyword(s):  
Life Table ◽  
Lower Risk ◽  
Clotting Factor ◽  
Rank Test ◽  
Life Table Method ◽  
Table Method ◽  
Log Rank Test ◽  
Free Interval ◽  
Post Infusion ◽  
Clotting Factor Concentrates

SummaryPost-infusion hepatitis is known to occur very frequently in haemophiliacs after treatment with unheated commercial clotting factor concentrates, obtained from large plasma donation pool. On the contrary, single-donor cryoprecipitate is likely to carry a lower risk of transmitting hepatitis.To evaluate this hypothesis, we retrospectively reviewed the medical records of 25 first infused haemophiliacs (from 1981 to 1984) treated with unheated commercial clotting factor concentrates (n = 19) or cryoprecipitate (n = 6).The hepatitis-free interval after the beginning of therapy was expressed as exposure days. The end point of each patient, i.e. the hepatitis occurrence, was defined as an increase of aminotransferases (ALT and AST) and/or the seroconversion of HBV-markers, which were checked every three months.The life-table method and log-rank test showed that cryo-precipitates had a significantly longer hepatitis-free interval (p = 0.0131, log-rank test) and a lower risk of transmitting hepatitis (p = 0.01-0.05, life-table method) than the commercial concentrates. However, the safety of cryoprecipitate therapy was shown to cover only a few exposure days, and so the real advantage of this product depends on the bleeding frequency of the patient concerned.We believe that these methods and our findings may be useful to assess and compare the safety of the new “heat-treated” clotting factor concentrates.

Non-surgical Treatments for Lung Metastases in Patients with soft Tissue Sarcoma: Stereotactic Body Radiation Therapy (SBRT) and Radiofrequency Ablation (RFA)

2020 ◽  
Vol 16 ◽  
Author(s):  
Cecilia Tetta ◽  
Maria Carpenzano ◽  
Areej Tawfiq J Algargoush ◽  
Marwah Algargoosh ◽  
Francesco Londero ◽  
...  
Keyword(s):  
Overall Survival ◽  
Radiation Therapy ◽  
Soft Tissue ◽  
Soft Tissue Sarcoma ◽  
Stereotactic Body Radiation Therapy ◽  
Lung Metastases ◽  
Disease Free Interval ◽  
Stereotactic Body Radiation ◽  
Free Interval ◽  
Disease Free

Background: Radio-frequency ablation (RFA) and Stereotactic Body Radiation Therapy (SBRT) are two emerging therapies for lung metastases. Introduction: We performed a literature review to evaluate outcomes and complications of these procedures in patients with lung metastases from soft tissue sarcoma (STS). Method: After selection, seven studies were included for each treatment encompassing a total of 424 patients: 218 in the SBRT group and 206 in the RFA group. Results: The mean age ranged from 47.9 to 64 years in the SBRT group and from 48 to 62.7 years in the RFA group. The most common histologic subtype was, in both groups, leiomyosarcoma. : In the SBRT group, median overall survival ranged from 25.2 to 69 months and median disease-free interval from 8.4 to 45 months. Two out of seven studies reported G3 and one G3 toxicity, respectively. In RFA patients, overall survival ranged from 15 to 50 months. The most frequent complication was pneumothorax. : Local control showed high percentage for both procedures. Conclusion: SBRT is recommended in patients unsuitable to surgery, in synchronous bilateral pulmonary metastases, in case of deep lesions and in patients receiving high-risk systemic therapies. RFA is indicated in case of a long disease-free interval, in oligometastatic disease, when only the lung is involved, in small size lesions far from large vessels. : Further large randomized studies are necessary to establish whether these treatments may also represent a reliable alternative to surgery.

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