Nearly complete TME quality conundrum

TME quality in rectal cancer surgery

BACKGROUND The concept of total mesorectal excision has revolutionised rectal cancer surgery. TME reduces the rate of local recurrence and tumour associated mortality. However, in clinical trials only 50% of the removed rectal tumours have an optimal TME quality. PATIENTS During a period of 36 months we performed 103 rectal resections. The majority of patients (76%; 78/103) received an anteri...

Embedding of Complete and Nearly Complete Binary Trees into Hypercubes

A new simple algorithm for optimal embedding of complete binary trees into hypercubes as well as a node-by-node algorithm for embedding of nearly complete binary trees into hypercubes are presented.

Jacobians of nearly complete and threshold graphs

The Jacobian of a graph, also known as the Picard Group, Sandpile Group, or Critical Group, is a discrete analogue of the Jacobian of an algebraic curve. It is known that the order of the Jacobian of a graph is equal to its number of spanning trees, but the exact structure is known for only a few classes of graphs. In this paper, we compute the Jacobian for graphs of the form Kn\E(H) where H is...

Nonorientable Genus of Nearly Complete Bipartite Graphs

Saturation Numbers for Nearly Complete Graphs

An upper bound on the saturation number for graphs as well as associated extremal graphs was given by (Kászonyi and Tuza in J. Graph Theory, 10:203–210, 1986). A minor improvement of that result, which was implied in their paper, will be stated. Using this result, a series of exact saturation numbers and associated extremal graphs will be proved for the nearly complete graphs Kt − E(L), where L...