Using a transgenic mouse model expressing the E2F1 gene under the control of a keratin 5 (K5) promoter, we previously demonstrated that increased E2F1 activity can promote tumorigenesis by cooperating with either a v-Ha-ras transgene to induce benign skin papillomas or p53 deficiency to induce spontaneous skin carcinomas. We now report that as K5 E2F1 transgenic mice age, they are predisposed t...

We prove the thrackle conjecture for K5 and K3,3. To do this we reduce the problem to a set of simultaneous quadratic equations over Z2. Parts of this proof are computer assisted.

Development of basal cell carcinomas (BCCs) in skin is associated with uncontrolled Sonic hedgehog (Shh) signaling, which operates primarily through the Gli family of transcription factors. Gli2 is a mediator of physiological Shh signaling in skin and is sufficient to produce BCCs when overexpressed by use of a Keratin 5 (K5) promoter. Analysis of Gli protein deletion mutants has identified an ...

Zarankiewicz’s Conjecture (ZC) states that the crossing number cr(Km,n) equals Z(m,n) := bm2 cb m−1 2 cb n 2 cb n−1 2 c. Since Kleitman’s verification of ZC for K5,n (from which ZC for K6,n easily follows), very little progress has been made around ZC; the most notable exceptions involve computer-aided results. With the aim of gaining a more profound understanding of this notoriously difficult ...

We show that the reachability problem for directed graphs that are either K3,3-free or K5-free is in unambiguous log-space, UL ∩ coUL. This significantly extends the result of Bourke, Tewari, and Vinodchandran that the reachability problem for directed planar graphs is in UL ∩ coUL. Our algorithm decomposes the graphs into biconnected and triconnected components. This gives a tree structure on ...

We show that the reachability problem for directed graphs that are either K3,3-free or K5-free is in unambiguous log-space, UL ∩ coUL. This significantly extends the result of Bourke, Tewari, and Vinodchandran that the reachability problem for directed planar graphs is in UL ∩ coUL. Our algorithm decomposes the graphs into biconnected and triconnected components. This gives a tree structure on ...

We show that the reachability problem for directed graphs that are either K3,3-free or K5-free is in unambiguous log-space, UL∩ coUL. This significantly extends the result of Bourke, Tewari, and Vinodchandran that the reachability problem for directed planar graphs is in UL∩ coUL. Our algorithm decomposes the graphs into biconnected and triconnected components. This gives a tree structure on th...

A control rod K5 of the 10 MW Budapest Research Reactor was damaged in 2004. We have applied both neutron and X-ray radiography to study the distribution of the residual material in the damaged K5. X-ray radiography visualized the main distribution of the residual materials, like different kinds of B4C and water, and the frozen gas bubbles, while neutron radiography displayed the fine structure...

We prove that the minimum weight of a dicycle is equal to the maximum number of disjoint dicycle covers, for every weighted digraph whose underlying graph is planar and does not have K5 − e as a minor (K5 − e is the complete graph on five vertices, minus one edge). Equality was previously known when forbidding K4 as a minor, while an infinite number of weighted digraphs show that planarity does...