Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Coloring decompositions of complete geometric graphs   A decomposition of a non-empty simple graph $G$ is a pair $[G,P]$, such that
$P$ is a set of non-empty induced subgraphs of $G$, and every edge of $G$
belongs to exactly one subgraph in $P$. The chromatic index $\chi'([G,P])$ of a
decomposition $[G,P]$ is the smallest number $k$ for which there exists a
$k$-coloring of the elements of $P$ in such a way that: for every element of
$P$ all of its edges have the same color, and if two members of $P$ share at
least one vertex, then they have different colors. A long standing conjecture
of Erd\H{o}s-Faber-Lov\'asz states that every decomposition $[K_n,P]$ of the
complete graph $K_n$ satisfies $\chi'([K_n,P])\leq n$. In this paper we work
with geometric graphs, and inspired by this formulation of the conjecture, we
introduce the concept of chromatic index of a decomposition of the complete
geometric graph. We present bounds for the chromatic index of several types of
decompositions when the vertices of the graph are in general position. We also
consider the particular case in which the vertices are in convex position and
present bounds for the chromatic index of a few types of decompositions.

18
The categories of this paper are: econ
23
The categories of this paper are: solv-int
21
The categories of this paper are: adap-org
7
The categories of this paper are: hep-th
30
The categories of this paper are: q-alg
15
The categories of this paper are: nucl-ex
22
The categories of this paper are: chao-dyn
1
The categories of this paper are: cs
14
The categories of this paper are: math-ph
3
The categories of this paper are: physics
25
The categories of this paper are: patt-sol
16
The categories of this paper are: stat
13
The categories of this paper are: quant-ph
24
The categories of this paper are: dg-ga
27
The categories of this paper are: comp-gas
12
The categories of this paper are: nucl-th