Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Hamiltonicity of bi-power of bipartite graphs, for finite and infinite
  cases   For a graph $G$, the $t$-th power $G^t$ is the graph on $V(G)$ such that two
vertices are adjacent if and only if they have distance at most $t$ in $G$; and
the $t$-th bi-power $G_B^t$ is the graph on $V(G)$ such that two vertices are
adjacent if and only if their distance in $G$ is odd at most $t$. Fleischner's
theorem states that the square of every 2-connected finite graph has a
Hamiltonian cycle. Georgakopoulos prove that the square of every 2-connected
infinite locally finite graph has a Hamiltonian circle. In this paper, we
consider the Hamiltonicity of the bi-power of bipartite graphs. We show that
for every connected finite bipartite graph $G$ with a perfect matching, $G_B^3$
has a Hamiltonian cycle. We also show that if $G$ is a connected infinite
locally finite bipartite graph with a perfect matching, then $G_B^3$ has a
Hamiltonian circle.

5
The categories of this paper are: gr-qc
19
The categories of this paper are: eess
16
The categories of this paper are: stat
3
The categories of this paper are: physics
26
The categories of this paper are: bayes-an
12
The categories of this paper are: nucl-th
0
The categories of this paper are: hep-ph
29
The categories of this paper are: funct-an
27
The categories of this paper are: comp-gas
28
The categories of this paper are: alg-geom
21
The categories of this paper are: adap-org
20
The categories of this paper are: acc-phys
33
The categories of this paper are: plasm-ph
1
The categories of this paper are: cs
34
The categories of this paper are: chem-ph
35
The categories of this paper are: mtrl-th