There is no universal countable random-free graph

There is no universal countable random-free graph

We consider embeddings between infinite graphs. In particular, We establish that there is no universal element in the class of countable graphs into which the random graph is not embeddable.

There is no universal countable pentagon-free graph

No countable C,-free graph contains every countable C,-free graph as a subgraph, for n 2 4. For n = 4, this was proved earlier by J. Pach.

Random generations of the countable random graph

We consider random processes more general than those considered by Erdös and Rényi for generating the countable random graph. It is proved that, in the category sense, almost all random processes we consider generate the countable random graph with probability 1. Under a weak boundedness assumption we give a criterion for the random processes which generate the countable random graph almost sur...

There is no free lunch--really.

Reimbursement risks with radiologist extenders: there is no free lunch!

There is great allure in the concept of using qualified health care providers to assist radiologists and radiation oncologists, increasing efficiency and possibly even improving patient care delivery. However, physician services are most commonly reimbursed under a system that is resource based, and the physician work and practice expense components of reimbursement for existing procedure codes...