136 research outputs found
S-Packing Colorings of Cubic Graphs
Given a non-decreasing sequence of positive
integers, an {\em -packing coloring} of a graph is a mapping from
to such that any two vertices with color
are at mutual distance greater than , . This paper
studies -packing colorings of (sub)cubic graphs. We prove that subcubic
graphs are -packing colorable and -packing
colorable. For subdivisions of subcubic graphs we derive sharper bounds, and we
provide an example of a cubic graph of order which is not
-packing colorable
-Packing Coloring of Cubic Halin Graphs
Given a non-decreasing sequence of
positive integers, an -packing coloring of a graph is a partition of the
vertex set of into subsets such that
for each , the distance between any two distinct vertices
and in is at least . In this paper, we study the problem
of -packing coloring of cubic Halin graphs, and we prove that every cubic
Halin graph is -packing colorable. In addition, we prove that such
graphs are -packing colorable.Comment: 9 page
Graph Theory
This workshop focused on recent developments in graph theory. These included in particular recent breakthroughs on nowhere-zero flows in graphs, width parameters, applications of graph sparsity in algorithms, and matroid structure results
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