Conflict-free Incidence Coloring of Outer-1-planar Graphs

An incidence of a graph G is a vertex-edge pair ( v, e ) such that v is incidence with e . A conflict-free incidence coloring of a graph is a coloring of the incidences in such a way that two incidences ( u, e ) and ( v, f ) get distinct colors if and only if they conflict each other, i.e., (i) u =...

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Veröffentlicht in:Acta Mathematicae Applicatae Sinica Jg. 40; H. 4; S. 929 - 942
Hauptverfasser: Qi, Meng-ke, Zhang, Xin
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Berlin/Heidelberg Springer Berlin Heidelberg 01.10.2024
Springer Nature B.V
Ausgabe:English series
Schlagworte:
Algorithms
Apexes
Applications of Mathematics
Assignment problem
Coloring
Graph coloring
Graph theory
Graphs
Math Applications in Computer Science
Mathematical and Computational Physics
Mathematics
Mathematics and Statistics
Radio networks
Theoretical
05C10
outer-1-planar graph
incidence coloring
combinatorial algorithm
channel assignment problem
05C15
ISSN:0168-9673, 1618-3932
Online-Zugang:Volltext
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Zusammenfassung:An incidence of a graph G is a vertex-edge pair ( v, e ) such that v is incidence with e . A conflict-free incidence coloring of a graph is a coloring of the incidences in such a way that two incidences ( u, e ) and ( v, f ) get distinct colors if and only if they conflict each other, i.e., (i) u = v , (ii) uv is e or f , or (iii) there is a vertex w such that uw = e and vw = f . The minimum number of colors used among all conflict-free incidence colorings of a graph is the conflict-free incidence chromatic number. A graph is outer-1-planar if it can be drawn in the plane so that vertices are on the outer-boundary and each edge is crossed at most once. In this paper, we show that the conflict-free incidence chromatic number of an outer-1-planar graph with maximum degree Δ is either 2Δ or 2Δ + 1 unless the graph is a cycle on three vertices, and moreover, all outer-1-planar graphs with conflict-free incidence chromatic number 2Δ or 2Δ + 1 are completely characterized. An efficient algorithm for constructing an optimal conflict-free incidence coloring of a connected outer-1-planar graph is given.
Bibliographie:ObjectType-Article-1
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content type line 14
ISSN:0168-9673
1618-3932
DOI:10.1007/s10255-024-1033-7