Minimal Diameter Orientation of Complete Split Graph

Author(s):  
Liu Xiaoshan ◽  
Wang Qi ◽  
Liu Yuhui
Keyword(s):  
Author(s):  
Thomas Budzinski ◽  
Nicolas Curien ◽  
Bram Petri

1984 ◽  
Vol 27 (1) ◽  
pp. 43-47
Author(s):  
Chiê Nara ◽  
Iwao Sato

AbstractLet G be a split graph with the independent part IG and the complete part KG. Suppose that the Dilworth number of (IG, ≼) with respect to the vicinal preorder ≼ is two and that of (KG, ≼) is an integer k. We show that G has a specified graph Hk, defined in this paper, as an induced subgraph.


1993 ◽  
Vol 2 (4) ◽  
pp. 409-415 ◽  
Author(s):  
Paul Erdős ◽  
Edward T. Ordman ◽  
Yechezkel Zalcstein

To partition the edges of a chordal graph on n vertices into cliques may require as many as n2/6 cliques; there is an example requiring this many, which is also a threshold graph and a split graph. It is unknown whether this many cliques will always suffice. We are able to show that (1 − c)n2/4 cliques will suffice for some c > 0.


2019 ◽  
Vol 2019 ◽  
pp. 1-8 ◽  
Author(s):  
Yasuyuki Takai ◽  
Masaki Tanito ◽  
Kazunobu Sugihara ◽  
Akihiro Ohira

Purpose. To assess the safety and effectiveness of the single-layered inverted internal limiting membrane (ILM) flap technique for treating chronic, large, or highly myopic macular holes (MHs). Methods. The medical records of 20 eyes of 20 consecutive Japanese patients with large MHs n=6 (minimal diameter, >400 μm), chronic MHs n=2 (symptom duration, >24 months), MHs in high myopia n=11 (axial length, >26 mm), and MHs in a patient unable to maintain prone positioning postoperatively n=1 were reviewed retrospectively. All patients underwent 25-gauge pars plana vitrectomy and the temporal inverted ILM flap technique. A semicircular ILM notch was made temporally two disc diameters from the MH using a 25-gauge knife, and the ILM was peeled temporally to create a semicircular ILM flap using a 25-gauge forceps. The single-layered ILM flap was inverted in a nasal direction to cover the MH. When an epiretinal membrane (ERM) was present, it was peeled before the ILM flap was inverted. Results. The MHs closed successfully in all (100%) eyes postoperatively. In the MHs associated with an ERM, after hole closure, gradual foveal deformation occurred in both the area from which the ILM was not peeled and the ILM flap inverted side. Conclusions. The single-layered inverted ILM flap technique, a simple surgery to treat MHs, provides scaffolding for retinal gliosis and may facilitate bridge formation between the walls of the MH under the flap. Considering the 100% success rate of MH closure, this technique seems to be effective and safe for treating chronic, large, or highly myopic MHs and MHs in patients unable to maintain postoperative prone positioning. In the MHs associated with ERMs, gradual foveal deformation was observed after ERM peeling. Further studies are needed to minimize surgical complications and understand the mechanism of this technique. This trial is registered with UMIN000035091.


2020 ◽  
Vol 1569 ◽  
pp. 042074
Author(s):  
Fatanur Baity Tsulutsya ◽  
Evawati Alisah ◽  
Lailiy Kurnia Ilahi
Keyword(s):  

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