191 research outputs found
Full Orientability of the Square of a Cycle
Let D be an acyclic orientation of a simple graph G. An arc of D is called
dependent if its reversal creates a directed cycle. Let d(D) denote the number
of dependent arcs in D. Define m and M to be the minimum and the maximum number
of d(D) over all acyclic orientations D of G. We call G fully orientable if G
has an acyclic orientation with exactly k dependent arcs for every k satisfying
m <= k <= M. In this paper, we prove that the square of a cycle C_n of length n
is fully orientable except n=6.Comment: 7 pages, accepted by Ars Combinatoria on May 26, 201
Acyclic list edge coloring of outerplanar graphs
AbstractAn acyclic list edge coloring of a graph G is a proper list edge coloring such that no bichromatic cycles are produced. In this paper, we prove that an outerplanar graph G with maximum degree Ξβ₯5 has the acyclic list edge chromatic number equal to Ξ
The strong chromatic index of 1-planar graphs
The chromatic index of a graph is the smallest for which
admits an edge -coloring such that any two adjacent edges have distinct
colors. The strong chromatic index of is the smallest such
that has a proper edge -coloring with the condition that any two edges
at distance at most 2 receive distinct colors. A graph is 1-planar if it can be
drawn in the plane so that each edge is crossed by at most one other edge.
In this paper, we show that every graph with maximum average degree
has . As a corollary, we
prove that every 1-planar graph with maximum degree has
, which improves a result, due to Bensmail et
al., which says that if
A note on the adjacent vertex distinguishing total chromatic number of graphs
AbstractAn adjacent vertex distinguishing total coloring of a graph G is a proper total coloring of G such that any pair of adjacent vertices have different sets of colors. The minimum number of colors needed for such a total coloring of G is denoted by Οaβ³(G). In this note, we show that Οaβ³(G)β€2Ξ for any graph G with maximum degree Ξβ₯3
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