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New classes of panchromatic digraphs
A digraph with a -colouring of its arcs is said to have a -kernel if there exists a subset of such that there are no monochromatic -paths for any two vertices , but for every , there exists a vertex such that there is a monochromatic -path in . The panchromatic number, , of is the greatest integer f...
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Published in: | AKCE International Journal of Graphs and Combinatorics 2015-11, Vol.12 (2-3), p.261-270 |
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Main Authors: | , |
Format: | Article |
Language: | English |
Subjects: | |
Citations: | Items that this one cites Items that cite this one |
Online Access: | Get full text |
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Summary: | A digraph
with a
-colouring of its arcs
is said to have a
-kernel if there exists a subset
of
such that there are no monochromatic
-paths for any two vertices
, but for every
, there exists a vertex
such that there is a monochromatic
-path in
. The panchromatic number,
, of
is the greatest integer
for which
has a
-kernel for every possible
-colouring of its arcs.
is said to be a panchromatic digraph if, for every
and every
-colouring
,
has a
-kernel. In this paper we study the panchromaticity of cycles. In particular, we show that even cycles are panchromatic and that
when
is an odd cycle. We also set sufficient conditions, in terms of its induced subdigraphs, for a digraph
to be panchromatic, and we show through counterexamples that these results cannot be improved. |
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ISSN: | 0972-8600 2543-3474 |
DOI: | 10.1016/j.akcej.2015.11.006 |