Edge-pancyclic block-intersection graphs

AbstractIt is shown that the block-intersection graph of both a balanced incomplete block design with block size at least 3 and λ = 1, and a transversal design is edge-pancyclic

Searching and sweeping graphs: a brief survey

This papers surveys some of the work done on trying to capture an intruder in a graph. If the intruder may be located only at vertices, the term searching is employed. If the intruder may be located at vertices or along edges, the term sweeping is employed. There are a wide variety of applications for searching and sweeping. Old results, new results and active research directions are discussed

Sweeping graphs with large clique number

AbstractSearching a network for intruders is an interesting and often difficult problem. Sweeping (or edge searching) is one such search model, in which intruders may exist anywhere along an edge. It was conjectured that graphs exist for which the connected sweep number is strictly less than the monotonic connected sweep number. We prove that this is true, and the difference can be arbitrarily large. We also show that the clique number is a lower bound on the sweep number

On factorisations of complete graphs into circulant graphs and the Oberwolfach problem

Various results on factorisations of complete graphs into circulant graphs and on 2-factorisations of these circulant graphs are proved. As a consequence, a number of new results on the Oberwolfach Problem are obtained. For example, a complete solution to the Oberwolfach Problem is given for every 2-regular graph of order 2p where p ≡ 5 (mod 8) is prime

Stromal senescence establishes an immunosuppressive microenvironment that drives tumorigenesis

Age is a significant risk factor for the development of cancer. However, the mechanisms that drive age-related increases in cancer remain poorly understood. To determine if senescent stromal cells influence tumorigenesis, we develop a mouse model that mimics the aged skin microenvironment. Using this model, here we find that senescent stromal cells are sufficient to drive localized increases in suppressive myeloid cells that contributed to tumour promotion. Further, we find that the stromal-derived senescence-associated secretory phenotype factor interleukin-6 orchestrates both increases in suppressive myeloid cells and their ability to inhibit anti-tumour T-cell responses. Significantly, in aged, cancer-free individuals, we find similar increases in immune cells that also localize near senescent stromal cells. This work provides evidence that the accumulation of senescent stromal cells is sufficient to establish a tumour-permissive, chronic inflammatory microenvironment that can shelter incipient tumour cells, thus allowing them to proliferate and progress unabated by the immune system