Some Results on Cyclic Interval Edge Colorings of Graphs
release_a5pjmipz2zft3kdh4iwvuknque
by
Armen S. Asratian, Carl Johan Casselgren, Petros A. Petrosyan
2017
Abstract
A proper edge coloring of a graph G with colors 1,2,...,t is called a
cyclic interval t-coloring if for each vertex v of G the edges
incident to v are colored by consecutive colors, under the condition that
color 1 is considered as consecutive to color t. We prove that a bipartite
graph G with even maximum degree Δ(G)≥ 4 admits a cyclic interval
Δ(G)-coloring if for every vertex v the degree d_G(v) satisfies
either d_G(v)≥Δ(G)-2 or d_G(v)≤ 2. We also prove that every
Eulerian bipartite graph G with maximum degree at most 8 has a cyclic
interval coloring. Some results are obtained for (a,b)-biregular graphs, that
is, bipartite graphs with the vertices in one part all having degree a and
the vertices in the other part all having degree b; it has been conjectured
that all these have cyclic interval colorings. We show that all
(4,7)-biregular graphs as well as all (2r-2,2r)-biregular (r≥ 2)
graphs have cyclic interval colorings. Finally, we prove that all complete
multipartite graphs admit cyclic interval colorings; this settles in the
affirmative, a conjecture of Petrosyan and Mkhitaryan.
In text/plain
format
Archived Files and Locations
application/pdf 242.5 kB
file_hqhbgn7wrnfetop33twa5jmuni
|
arxiv.org (repository) web.archive.org (webarchive) |
1606.09389v2
access all versions, variants, and formats of this works (eg, pre-prints)