Partitioning a graph into highly connected subgraphs

Given $k\ge 1$, a $k$-proper partition of a graph $G$ is a partition ${\mathcal P}$ of $V(G)$ such that each part $P$ of ${\mathcal P}$ induces a $k$-connected subgraph of $G$. We prove that if $G$ is a graph of order $n$ such that $\delta(G)\ge \sqrt{n}$, then $G$ has a $2$-proper partition with at most $n/\delta(G)$ parts. The bounds on the number of parts and the minimum degree are both best possible. We then prove that If $G$ is a graph of order $n$ with minimum degree $\delta(G)\ge\sqrt{c(k-1)n}$, where $c=\frac{2123}{180}$, then $G$ has a $k$-proper partition into at most $\frac{cn}{\delta(G)}$ parts. This improves a result of Ferrara, Magnant and Wenger [Conditions for Families of Disjoint $k$-connected Subgraphs in a Graph, Discrete Math. 313 (2013), 760--764] and both the degree condition and the number of parts are best possible up to the constant $c$

Novel Mutation in a Patient with Cholesterol Ester Storage Disease

Cholesterol ester storage disease (CESD) is a chronic liver disease that typically presents with hepatomegaly. It is characterized by hypercholesterolemia, hypertriglyceridemia, high-density lipoprotein deficiency, and abnormal lipid deposition within multiple organs. It is an autosomal recessive disease that is due to a deficiency in lysosomal acid lipase (LAL) activity, which is coded by the lysosomal acid lipase gene (LIPA). We describe the case of a 5-year-old south Asian female incidentally found to have hepatomegaly, and subsequent workup confirmed the diagnosis of CESD. DNA sequencing confirmed the presence of a novel hepatic mutation. It is a four-nucleotide deletion c.57_60delTGAG in exon 2 of the LIPA gene. This mutation is predicted to result in a premature translation stop downstream of the deletion (p.E20fs) and, therefore, is felt to be a disease-causing mutation