Browsing by Author "Reed, Bruce"
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Acyclic edge colourings of graphs with large girth
Cai, Xing Shi; Perarnau Llobet, Guillem; Reed, Bruce; Watts, Adam Bene (20161103)
Article
Open AccessAn edge colouring of a graph G is called acyclic if it is proper and every cycle contains at least three colours. We show that for every e > 0, there exists a g = g(e) such that if G has maximum degree ¿ and girth at least ... 
Existence of spanning Ffree subgraphs with large minimum degree
Perarnau Llobet, Guillem; Reed, Bruce (20161207)
Article
Restricted access  publisher's policyLet F be a family of graphs and let d be large enough. For every dregular graph G, we study the existence of a spanning Ffree subgraph of G with large minimum degree. This problem is well understood if F does not contain ... 
How to determine if a random graph with a fixed degree sequence has a giant component
Joos, Felix; Perarnau Llobet, Guillem; Rautenbach, Dieter; Reed, Bruce (Institute of Electrical and Electronics Engineers (IEEE), 2016)
Conference report
Open AccessThe traditional ErdosRenyi model of a random network is of little use in modelling the type of complex networks which modern researchers study. In this graph, every pair of vertices is equally likely to be connected by ... 
How to determine if a random graph with a fixed degree sequence has a giant component
Joos, Felix; Perarnau Llobet, Guillem; Rautenbach, Dieter; Reed, Bruce (20170126)
Article
Open AccessFor a fixed degree sequence D=(d1,…,dn) , let G(D) be a uniformly chosen (simple) graph on {1,…,n} where the vertex i has degree di . In this paper we determine whether G(D) has a giant component with high probability, ...