Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Partitioning two-coloured complete multipartite graphs into
  monochromatic paths and cycles   We show that any complete $k$-partite graph $G$ on $n$ vertices, with $k \ge
3$, whose edges are two-coloured, can be covered with two vertex-disjoint
monochromatic paths of distinct colours. We prove this under the necessary
assumption that the largest partition class of $G$ contains at most $n/2$
vertices. This extends known results for complete and complete bipartite
graphs.
  Secondly, we show that in the same situation, all but $o(n)$ vertices of the
graph can be covered with two vertex-disjoint monochromatic cycles of distinct
colours, if colourings close to a split colouring are excluded. From this we
derive that the whole graph, if large enough, may be covered with 14
vertex-disjoint monochromatic cycles.

9
The categories of this paper are: nlin
16
The categories of this paper are: stat
33
The categories of this paper are: plasm-ph
35
The categories of this paper are: mtrl-th
7
The categories of this paper are: hep-th
22
The categories of this paper are: chao-dyn
14
The categories of this paper are: math-ph
5
The categories of this paper are: gr-qc
4
The categories of this paper are: cond-mat
23
The categories of this paper are: solv-int
8
The categories of this paper are: hep-ex
32
The categories of this paper are: atom-ph
36
The categories of this paper are: cmp-lg
25
The categories of this paper are: patt-sol
37
The categories of this paper are: supr-con
27
The categories of this paper are: comp-gas