33,992 research outputs found
Quantum statistics on graphs
Quantum graphs are commonly used as models of complex quantum systems, for
example molecules, networks of wires, and states of condensed matter. We
consider quantum statistics for indistinguishable spinless particles on a
graph, concentrating on the simplest case of abelian statistics for two
particles. In spite of the fact that graphs are locally one-dimensional, anyon
statistics emerge in a generalized form. A given graph may support a family of
independent anyon phases associated with topologically inequivalent exchange
processes. In addition, for sufficiently complex graphs, there appear new
discrete-valued phases. Our analysis is simplified by considering combinatorial
rather than metric graphs -- equivalently, a many-particle tight-binding model.
The results demonstrate that graphs provide an arena in which to study new
manifestations of quantum statistics. Possible applications include topological
quantum computing, topological insulators, the fractional quantum Hall effect,
superconductivity and molecular physics.Comment: 21 pages, 6 figure
Maximum Independent Sets in Subcubic Graphs: New Results
The maximum independent set problem is known to be NP-hard in the class of
subcubic graphs, i.e. graphs of vertex degree at most 3. We present a
polynomial-time solution in a subclass of subcubic graphs generalizing several
previously known results
Short Cycle Covers of Cubic Graphs and Graphs with Minimum Degree Three
The Shortest Cycle Cover Conjecture of Alon and Tarsi asserts that the edges
of every bridgeless graph with edges can be covered by cycles of total
length at most . We show that every cubic bridgeless graph has a
cycle cover of total length at most and every bridgeless
graph with minimum degree three has a cycle cover of total length at most
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