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- Henry Liu, Robert Morris, Noah Prince
- Discrete Mathematics
- 2008

Suppose the edges of the complete graph on n vertices, E(K n), are coloured using r colours; how large a k-connected sub-graph are we guaranteed to find, which uses only at most s of the colours? This question is due to Bollobás, and the case s = 1 was considered in [3]. Here we shall consider the case s 2, proving in particular that when s = 2 and r + 1 is… (More)

- Henry Liu, Robert Morris, Noah Prince
- Journal of Graph Theory
- 2009

We consider the following question of Bollobás: given an r-colouring of E(K n), how large a k-connected subgraph can we find using at most s colours? We provide a partial solution to this problem when s = 1 (and n is not too small), showing that when r = 2 the answer is n − 2k + 2, when r = 3 the answer is ⌊ n−k 2 ⌋ + 1 or ⌈ n−k 2 ⌉ + 1, and when r − 1 is a… (More)

- Shinya Fujita, Henry Liu
- SIAM J. Discrete Math.
- 2010

The balanced decomposition number f (G) of a graph G was introduced by Fujita and Nakamigawa [Discr. A balanced colouring of a graph G is a colouring of some of the ver-tices of G with two colours, such that there is the same number of vertices in each colour. Then, f (G) is the minimum integer s with the following property: For any balanced colouring of G,… (More)

An edge-coloured path is rainbow if the colours of its edges are distinct. For a positive integer k, an edge-colouring of a graph G is rainbow k-connected if any two vertices of G are connected by k internally vertex-disjoint rainbow paths. The rainbow k-connection number rc k (G) is defined to be the minimum integer t such that there exists an… (More)

- Henry Liu, Teresa Sousa
- 2013

Given graphs G and H, and a colouring of the edges of G with k colours, a monochromatic H-decomposition of G is a partition of the edge set of G such that each part is either a single edge or forms a monochromatic graph isomorphic to H. Let φ k (n, H) be the smallest number φ such that any k-edge-coloured graph G of order n, admits a monochromatic… (More)

- Henry Liu, Angela Mestre, Teresa Sousa
- Discrete Applied Mathematics
- 2013

- Shinya Fujita, Henry Liu
- Discussiones Mathematicae Graph Theory
- 2013

A balanced colouring of a graph G is a colouring of some of the vertices of G with two colours, say red and blue, such that there is the same number of vertices in each colour. The balanced decomposition number f (G) of G is the minimum integer s with the following property: For any balanced colouring of G, there is a partition V (G) = V 1 ˙ ∪ · · · ˙ ∪ V r… (More)

- Henry Liu, Lisa Sangkum, Geoffrey Liu, Michael Green, Marilyn Li, Alan Kaye
- Journal of biomedical research
- 2016

Epinephrine is often used for the treatment of patients with heart failure, low cardiac output and cardiac arrest. It can acutely improve hemodynamic parameters; however, it does not seem to improve longer term clinical outcomes. Therefore, we hypothesized that epinephrine may induce unfavorable changes in gene expression of cardiomyocyte. Thus, we… (More)

- Henry Liu
- 2013

Wireless power transfer has been a dream sought after ever since the discovery of electricity. Beginning with electromagnetic induction, physicists and engineers have attempted to increase the efficiency with which electrical power can be transferred through the air. Recently, a team of scientists at MIT found that by adding a capacitor in parallel with the… (More)

- Frank Ralbovsky, Henry Liu
- 2004

Authority (hereafter " NYSERDA). The opinions expressed in this report do not necessarily reflect those of NYSERDA or the State of New York, and reference to any specific product, service, process, or method does not constitute an implied or expressed recommendation or endorsement of it. Further, NYSERDA, the State of New York, and the contractor make no… (More)