Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Tight Bound for Conflict-free Coloring in terms of Distance to Cluster   Given an undirected graph $G = (V,E)$, a conflict-free coloring with respect
to open neighborhoods (CFON coloring) is a vertex coloring such that every
vertex has a uniquely colored vertex in its open neighborhood. The minimum
number of colors required for such a coloring is the CFON chromatic number of
$G$, denoted by $\chi_{ON}(G)$.
  In previous work [WG 2020], we showed the upper bound $\chi_{ON}(G) \leq
dc(G) + 3$, where $dc(G)$ denotes the distance to cluster parameter of $G$. In
this paper, we obtain the improved upper bound of $\chi_{ON}(G) \leq dc(G) +
1$. We also exhibit a family of graphs for which $\chi_{ON}(G) > dc(G)$,
thereby demonstrating that our upper bound is tight.

23
The categories of this paper are: solv-int
30
The categories of this paper are: q-alg
20
The categories of this paper are: acc-phys
13
The categories of this paper are: quant-ph
1
The categories of this paper are: cs
24
The categories of this paper are: dg-ga
36
The categories of this paper are: cmp-lg
37
The categories of this paper are: supr-con
10
The categories of this paper are: q-bio
12
The categories of this paper are: nucl-th
6
The categories of this paper are: astro-ph
29
The categories of this paper are: funct-an
35
The categories of this paper are: mtrl-th
22
The categories of this paper are: chao-dyn
4
The categories of this paper are: cond-mat
28
The categories of this paper are: alg-geom