Abstract
AbstractA 1-removed subgraph $$G_f$$
G
f
of a graph $$G=(V,E)$$
G
=
(
V
,
E
)
is obtained by
(i)
selecting at most one edge f(v) for each vertex $$v\in V$$
v
∈
V
, such that $$v\in f(v)\in E$$
v
∈
f
(
v
)
∈
E
(the mapping $$f:V\rightarrow E \cup \{\varnothing \}$$
f
:
V
→
E
∪
{
∅
}
is allowed to be non-injective), and
(ii)
deleting all the selected edges f(v) from the edge set E of G.
Proper vertex colorings of 1-removed subgraphs proved to be a useful tool for earlier research on some Turán-type problems. In this paper, we introduce a systematic investigation of the graph invariant 1-robust chromatic number, denoted as $$\chi _1(G)$$
χ
1
(
G
)
. This invariant is defined as the minimum chromatic number $$\chi (G_f)$$
χ
(
G
f
)
among all 1-removed subgraphs $$G_f$$
G
f
of G. We also examine other standard graph invariants in a similar manner.
Funder
Nemzeti Kutatási Fejlesztési és Innovációs Hivatal
Publisher
Springer Science and Business Media LLC
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