Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Hamiltonian problem and $t$-path traceable graphs   The problem of characterizing maximal non-Hamiltonian graphs may be naturally
extended to characterizing graphs that are maximal with respect to
non-traceability and beyond that to $t$-path traceability. We show how
traceability behaves with respect to disjoint union of graphs and the join with
a complete graph. Our main result is a decomposition theorem that reduces the
problem of characterizing maximal $t$-path traceable graphs to characterizing
those that have no universal vertex. We generalize a construction of maximal
non-traceable graphs by Zelinka to $t$-path traceable graphs.

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The categories of this paper are: atom-ph
8
The categories of this paper are: hep-ex
24
The categories of this paper are: dg-ga
16
The categories of this paper are: stat
13
The categories of this paper are: quant-ph
26
The categories of this paper are: bayes-an
34
The categories of this paper are: chem-ph
3
The categories of this paper are: physics
27
The categories of this paper are: comp-gas
12
The categories of this paper are: nucl-th
19
The categories of this paper are: eess
4
The categories of this paper are: cond-mat
22
The categories of this paper are: chao-dyn
6
The categories of this paper are: astro-ph
5
The categories of this paper are: gr-qc
7
The categories of this paper are: hep-th