The Infona portal uses cookies, i.e. strings of text saved by a browser on the user's device. The portal can access those files and use them to remember the user's data, such as their chosen settings (screen view, interface language, etc.), or their login data. By using the Infona portal the user accepts automatic saving and using this information for portal operation purposes. More information on the subject can be found in the Privacy Policy and Terms of Service. By closing this window the user confirms that they have read the information on cookie usage, and they accept the privacy policy and the way cookies are used by the portal. You can change the cookie settings in your browser.
In this paper, we deal with the notion of star coloring of graphs. A star coloring of an undirected graph G is a proper vertex coloring of G (i.e., no two neighbors are assigned the same color) such that any path of length 3 in G is not bicolored. We give the exact value of the star chromatic number of different families of graphs such as trees, cycles, complete bipartite graphs, outerplanar...
We discuss the space of mappings f from the vertices of a fixed graph G to Z which satisfy: |f(u)-f(v)|=<1 whenever uv E(G). In particular, we focus on the (random) range of such mappings.
In a simple graph, we consider the minimum number of edges which hit all the odd cycles and the maximum number of edge-disjoint odd cycles. When these two coefficients are equal, interesting questions can be posed. Related problems, but interchanging ‘vertex-disjoint’ and ‘edge-disjoint’, have been studied by Berge and Fouquet (Discrete Math. 169 (1997) 169–176.)
Set the date range to filter the displayed results. You can set a starting date, ending date or both. You can enter the dates manually or choose them from the calendar.