An oriented coloring of graphs with maximum average degree less than
نویسنده
چکیده
An oriented k-coloring of an oriented graph G is a homomorphism from G to an oriented graph H of order k. We prove that every oriented graph with maximum average degree less than 10 3 has an oriented chromatic number at most 16. This implies that every oriented planar graph with girth at least five has an oriented chromatic number at most 16, that improves the previous known bound of 19 due to Borodin et al. [Borodin, O. V. and Kostochka, A. V. and Nešetřil, J. and Raspaud, A. and Sopena, É., On the maximum average degree and the oriented chromatic number of a graph, Discrete Math., 77–89, 206, 1999].
منابع مشابه
k-forested choosability of graphs with bounded maximum average degree
A proper vertex coloring of a simple graph is $k$-forested if the graph induced by the vertices of any two color classes is a forest with maximum degree less than $k$. A graph is $k$-forested $q$-choosable if for a given list of $q$ colors associated with each vertex $v$, there exists a $k$-forested coloring of $G$ such that each vertex receives a color from its own list. In this paper, we prov...
متن کاملAn oriented coloring of planar graphs with girth at least five
An oriented k-coloring of an oriented graph G is a homomorphism from G to an oriented graph H of order k. We prove that every oriented graph with maximum average degree strictly less than 10 3 has an oriented chromatic number at most 16. This implies that every oriented planar graph with girth at least 5 has an oriented chromatic number at most 16, that improves the previous known bound of 19 d...
متن کاملList coloring the square of sparse graphs with large degree
We consider the problem of coloring the squares of graphs of bounded maximum average degree, that is, the problem of coloring the vertices while ensuring that two vertices that are adjacent or have a common neighbour receive different colors. Borodin et al. proved in 2004 and 2008 that the squares of planar graphs of girth at least seven and sufficiently large maximum degree ∆ are list (∆ + 1)-...
متن کاملIncidence coloring of graphs with high maximum average degree
An incidence of an undirected graph G is a pair (v, e) where v is a vertex of G and e an edge of G incident with v. Two incidences (v, e) and (w, f) are adjacent if one of the following holds: (i) v = w, (ii) e = f or (iii) vw = e or f . An incidence coloring of G assigns a color to each incidence of G in such a way that adjacent incidences get distinct colors. In 2005, Hosseini Dolama et al. [...
متن کاملDecomposition of sparse graphs, with application to game coloring number
Let k be a nonnegative integer, and let mk = 4(k+1)(k+3) k2+6k+6 . We prove that every simple graph with maximum average degree less than mk decomposes into a forest and a subgraph with maximum degree at most k. It follows that every simple graph with maximum average degree less than mk has game coloring number at most 4 + k.
متن کامل