978 research outputs found
A Rare Nasopharyngeal Foreign Body
Nasopharynx is an exceptionally rare anatomical location for foreign body impaction. We present a rare case of nasopharyngeal foreign body (NFB) in a 7 years old child. The diagnosis was confirmed by nasal endoscopy. Immediate removal of foreign body (FB) in the nasopharynx was performed under general anesthesia. This rare situation is potentially dangerous, since its dislodgment may cause fatal airway obstruction. Therefore, in all cases with missing foreign bodies in the aerodigestive system, nasopharyngeal impaction should be kept in mind and endoscopic examination of the region should be considere
Separation index of graphs and stacked 2-spheres
In 1987, Kalai proved that stacked spheres of dimension are
characterised by the fact that they attain equality in Barnette's celebrated
Lower Bound Theorem. This result does not extend to dimension . In this
article, we give a characterisation of stacked -spheres using what we call
the {\em separation index}. Namely, we show that the separation index of a
triangulated -sphere is maximal if and only if it is stacked. In addition,
we prove that, amongst all -vertex triangulated -spheres, the separation
index is {\em minimised} by some -vertex flag sphere for .
Furthermore, we apply this characterisation of stacked -spheres to settle
the outstanding -dimensional case of the Lutz-Sulanke-Swartz conjecture that
"tight-neighbourly triangulated manifolds are tight". For dimension ,
the conjecture has already been proved by Effenberger following a result of
Novik and Swartz.Comment: Some typos corrected, to appear in "Journal of Combinatorial Theory
A
Approximation bounds on maximum edge 2-coloring of dense graphs
For a graph and integer , an edge -coloring of is an
assignment of colors to edges of , such that edges incident on a vertex span
at most distinct colors. The maximum edge -coloring problem seeks to
maximize the number of colors in an edge -coloring of a graph . The
problem has been studied in combinatorics in the context of {\em anti-Ramsey}
numbers. Algorithmically, the problem is NP-Hard for and assuming the
unique games conjecture, it cannot be approximated in polynomial time to a
factor less than . The case , is particularly relevant in practice,
and has been well studied from the view point of approximation algorithms. A
-factor algorithm is known for general graphs, and recently a -factor
approximation bound was shown for graphs with perfect matching. The algorithm
(which we refer to as the matching based algorithm) is as follows: "Find a
maximum matching of . Give distinct colors to the edges of . Let
be the connected components that results when M is
removed from G. To all edges of give the th color."
In this paper, we first show that the approximation guarantee of the matching
based algorithm is for graphs with perfect matching
and minimum degree . For , this is better than the approximation guarantee proved in {AAAP}. For triangle free graphs
with perfect matching, we prove that the approximation factor is , which is better than for .Comment: 11pages, 3 figure
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