Tutte observed that every nowhere-zero k-flow on a plane graph gives rise to a kvertex-coloring of its dual, and vice versa. Thus nowhere-zero integer flow and graph coloring can be viewed as dual concepts. Jaeger further shows that if a graph G has a face-k-colorable 2-cell embedding in some orientable surface, then it has a nowhere-zero k-flow. However, if the surface is nonorientable, then a...

We have compared four computer-assisted methods to measure penetration of the femoral head into the acetabular component in total hip replacement. These were the Martell Hip Analysis suite 7.14, Rogan HyperOrtho, Rogan View Pro-X and Roman v1.70. The images used for the investigation comprised 24 anteroposterior digital radiographs and 24 conventional acetate radiographs which were scanned to p...

The Northamptonshire sites and monuments record currently contains 1573 records related to the Roman period, which constitutes 22.5% of the total. A large proportion of the undated cropmark sites are, however, also likely to be Roman and/or Iron Age in date and should be added to this total. In Northamptonshire this period is characterized by intensively occupied and large scale rural landscape...

This is a survey of the method of graph cuts and its applications to graph clustering of weighted unsigned and signed graphs. I provide a fairly thorough treatment of the method of normalized graph cuts, a deeply original method due to Shi and Malik, including complete proofs. I also cover briefly the method of ratio cuts, and show how it can be viewed as a special case of normalized cuts. I in...

In this paper, we present a novel method for constrained cluster size signed spectral clustering (CSS) which allows us to subdivide large groups of people based on their relationships. In general, signed clustering only requires K hard clusters and does not constrain the cluster sizes. We extend signed clustering to include cluster size constraints. Using an example of seating assignment, we ef...

A k-signed r-set on [n] = {1, ..., n} is an ordered pair (A, f), where A is an rsubset of [n] and f is a function from A to [k]. Families A1, ...,Ap are said to be cross-intersecting if any set in any family Ai intersects any set in any other family Aj . Hilton proved a sharp bound for the sum of sizes of cross-intersecting families of r-subsets of [n]. Our aim is to generalise Hilton's bound t...

This paper is devoted to the study of quadruple Roman domination in trees, and it a contribution Special Issue “Theoretical computer science discrete mathematics” Symmetry. For any positive integer k, [k]-Roman dominating function ([k]-RDF) simple graph G from vertex set V {0,1,2,…,k+1} if for u?V with f(u)<k, ?x?N(u)?{u}f(x)?|{x?N(u):f(x)?1}|+k, where N(u) open neighborhood u. The weight [k...

Roman kimli?i ve temsiline yönelik yakla??mlar, hem akademik mecrada de Romanlar aras?nda oldukça tart??mal?d?r. Etnik ba?lam? öne ç?kan kültürel kimli?i, ile Öteki (Gaco, olmayanlar) meydana gelen s?n?r ili?kileri arac?l???yla tesis edilmektedir. Bu in?a, heterojen bir kimlik getirmek yana, çat??mal? sürece i?aret etmektedir. Kültürel kimli?in kurulu?unda önemli etkisi olan grup içi çat??malar...