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.
Some exact results in generalized Ramsey theory are given — others are conjectured. For example, all known results for the Ramsey number of the cycle — complete graphs are presented with attention focused on the unsolved parts. Non-standard results include introduction of "edge minimal" graphs that "arrow" a pair of graphs.
A simple graph G on n vertices satisfies property Pi if between every pair of distinct vertices of G, there exists a path with i vertices. In this paper known results and open questions about the relationship between property Pi and property Pj are considered. There are degree conditions, edge conditions and the condition of being the power of a graph which guarantee that a graph is Hamiltonian-connected...
We consider several constructions of edge critical 4-chromatic graphs which can be written as the union of a bipartite graph and a matching. In particular we construct such a graph G with each of the following properties: G can be contracted to a given critical 4-chromatic graph; for each n ≥ 7, G has n vertices and three matching edges (it is also shown that such graphs must have at least $${{8n}...
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.