Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The tessellation problem of quantum walks   Quantum walks have received a great deal of attention recently because they
can be used to develop new quantum algorithms and to simulate interesting
quantum systems. In this work, we focus on a model called staggered quantum
walk, which employs advanced ideas of graph theory and has the advantage of
including the most important instances of other discrete-time models. The
evolution operator of the staggered model is obtained from a tessellation
cover, which is defined in terms of a set of partitions of the graph into
cliques. It is important to establish the minimum number of tessellations
required in a tessellation cover, and what classes of graphs admit a small
number of tessellations. We describe two main results: (1) infinite classes of
graphs where we relate the chromatic number of the clique graph to the minimum
number of tessellations required in a tessellation cover, and (2) the problem
of deciding whether a graph is $k$-tessellable for $k\ge 3$ is NP-complete.

21
The categories of this paper are: adap-org
0
The categories of this paper are: hep-ph
12
The categories of this paper are: nucl-th
8
The categories of this paper are: hep-ex
14
The categories of this paper are: math-ph
27
The categories of this paper are: comp-gas
5
The categories of this paper are: gr-qc
16
The categories of this paper are: stat
9
The categories of this paper are: nlin
22
The categories of this paper are: chao-dyn
26
The categories of this paper are: bayes-an
24
The categories of this paper are: dg-ga
23
The categories of this paper are: solv-int
36
The categories of this paper are: cmp-lg
33
The categories of this paper are: plasm-ph
29
The categories of this paper are: funct-an