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.
Gyárfás et al. and Zaker have proven that the Grundy number of a graph G satisfies Γ(G)≥t if and only if G contains an induced subgraph called a t-atom. The family of t-atoms has bounded order and contains a finite number of graphs. In this article, we introduce equivalents of t-atoms for b-coloring and partial Grundy coloring. This concept is used to prove that determining if φ(G)≥t and ∂Γ(G)≥t (under...
The Grundy number of a graph G, denoted by Γ(G), is the largest k such that there exists a partition of V(G), into k independent sets V1,…,Vk and every vertex of Vi is adjacent to at least one vertex in Vj, for every j<i. The objects which are studied in this article are families of r-regular graphs such that Γ(G)=r+1. Using the notion of independent module, a characterization of this family is...
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.