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pro vyhledávání: '"Dowden, Chris"'
We introduce a new positional game called `Toucher-Isolator', which is a quantitative version of a Maker-Breaker type game. The playing board is the set of edges of a given graph G, and the two players, Toucher and Isolator, claim edges alternately.
Externí odkaz:
http://arxiv.org/abs/1903.11411
We investigate the genus $g(n,m)$ of the Erd\H{o}s-R\'enyi random graph $G(n,m)$, providing a thorough description of how this relates to the function $m=m(n)$, and finding that there is different behaviour depending on which `region' $m$ falls into.
Externí odkaz:
http://arxiv.org/abs/1806.05468
For integers $g,m \geq 0$ and $n>0$, let $S_{g}(n,m)$ denote the graph taken uniformly at random from the set of all graphs on $\{1,2, \ldots, n\}$ with exactly $m=m(n)$ edges and with genus at most $g$. We use counting arguments to investigate the c
Externí odkaz:
http://arxiv.org/abs/1709.00864
Autor:
Dowden, Chris
We investigate the problem of obtaining agreement protocols in the presence of a mobile adversary, who can control an ever-changing selection of processors. We make improvements to previous results for the case when the communications network forms a
Externí odkaz:
http://arxiv.org/abs/1706.06789
Autor:
Dowden, Chris
We investigate the problem of reaching majority agreement in a disconnected network. We obtain conditions under which such an agreement is certainly possible/impossible, and observe that these coincide in the ternary case.
Comment: 5 pages
Comment: 5 pages
Externí odkaz:
http://arxiv.org/abs/1607.08352
Autor:
Dowden, Chris
Publikováno v:
Journal of Mathematical Cryptology (2015) 9, 205-214
We investigate the problem of secure message transmission in the presence of a "fully generalised" adversary, who disrupts and listens to separate sets of communication wires. We extend previous results by considering the case when these sets may hav
Externí odkaz:
http://arxiv.org/abs/1512.04393
Autor:
Dowden, Chris
We study the topic of "extremal" planar graphs, defining $\mathrm{ex_{_{\mathcal{P}}}}(n,H)$ to be the maximum number of edges possible in a planar graph on $n$ vertices that does not contain a given graph $H$ as a subgraph. In particular,we examine
Externí odkaz:
http://arxiv.org/abs/1512.04385
Autor:
Dowden, Chris
Random planar graphs have been the subject of much recent work. Many basic properties of the standard uniform random planar graph P_{n}, by which we mean a graph chosen uniformly at random from the set of all planar graphs with vertex set {1,2,...,n}
Externí odkaz:
http://arxiv.org/abs/1307.5727
Autor:
Dowden, Chris
Publikováno v:
Graphs and Combinatorics (2011)27:87-107
Let P_{n,d,D} denote the graph taken uniformly at random from the set of all labelled planar graphs on {1,2,...,n} with minimum degree at least d(n) and maximum degree at most D(n). We use counting arguments to investigate the probability that P_{n,d
Externí odkaz:
http://arxiv.org/abs/1101.5288
Autor:
Dowden, Chris
Publikováno v:
Discrete Mathematics 310 (19), 2546-2549 (2010)
In this paper, we investigate a problem concerning quartets, which are a particular type of tree on four leaves. Loosely speaking, a set of quartets is said to be `definitive' if it completely encapsulates the structure of some larger tree, and `mini
Externí odkaz:
http://arxiv.org/abs/1101.5302