232 research outputs found
On lower bounds for the matching number of subcubic graphs
We give a complete description of the set of triples (a,b,c) of real numbers
with the following property. There exists a constant K such that a n_3 + b n_2
+ c n_1 - K is a lower bound for the matching number of every connected
subcubic graph G, where n_i denotes the number of vertices of degree i for each
i
Fractional total colourings of graphs of high girth
Reed conjectured that for every epsilon>0 and Delta there exists g such that
the fractional total chromatic number of a graph with maximum degree Delta and
girth at least g is at most Delta+1+epsilon. We prove the conjecture for
Delta=3 and for even Delta>=4 in the following stronger form: For each of these
values of Delta, there exists g such that the fractional total chromatic number
of any graph with maximum degree Delta and girth at least g is equal to
Delta+1
On measurement-based quantum computation with the toric code states
We study measurement-based quantum computation (MQC) using as quantum
resource the planar code state on a two-dimensional square lattice (planar
analogue of the toric code). It is shown that MQC with the planar code state
can be efficiently simulated on a classical computer if at each step of MQC the
sets of measured and unmeasured qubits correspond to connected subsets of the
lattice.Comment: 9 pages, 5 figure
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