Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Tight Cuts in Bipartite Grafts I: Capital Distance Components   This paper is the first from a series of papers that provide a
characterization of maximum packings of $T$-cuts in bipartite graphs. Given a
connected graph, a set $T$ of an even number of vertices, and a minimum
$T$-join, an edge weighting can be defined, from which distances between
vertices can be defined. Furthermore, given a specified vertex called root,
vertices can be classified according to their distances from the root, and this
classification of vertices can be used to define a family of subgraphs called
{\em distance components}. Seb\"o provided a theorem that revealed a
relationship between distance components, minimum $T$-joins, and $T$-cuts. In
this paper, we further investigate the structure of distance components in
bipartite graphs. Particularly, we focus on {\em capital} distance components,
that is, those that include the root. We reveal the structure of capital
distance components in terms of the $T$-join analogue of the general
Kotzig-Lov\'asz canonical decomposition.

26
The categories of this paper are: bayes-an
28
The categories of this paper are: alg-geom
31
The categories of this paper are: ao-sci
9
The categories of this paper are: nlin
19
The categories of this paper are: eess
24
The categories of this paper are: dg-ga
34
The categories of this paper are: chem-ph
21
The categories of this paper are: adap-org
36
The categories of this paper are: cmp-lg
18
The categories of this paper are: econ
25
The categories of this paper are: patt-sol
27
The categories of this paper are: comp-gas
15
The categories of this paper are: nucl-ex
33
The categories of this paper are: plasm-ph
7
The categories of this paper are: hep-th
22
The categories of this paper are: chao-dyn