We will have a workshop on discrete mathematics and algorithms on 27-29 March, 2024.
Registration fees will be used for operational purposes, including WiFi access, coffee and other beverages that will be served during the breaks. Lunches and the dinner on the last day will incur separate charges, but since reservations are required, we will conduct a separate survey for them after fixing all participants.
For details, see here (registration link).
While formal accommodations are not provided by the organizer, we strongly recommend booking your stay at Ala Moana Hotel, which is in close proximity to the bus stop servicing the venue. Notably, both invited speakers and organizing committee members will be staying at this hotel. Additionally, we have scheduled supplementary meetings to take place there during the conference.
Title: Eternal Domination
AbstractWe consider a discrete-time, dynamic process in which the goal is to maintain a dominating set in a graph over an infinite sequence of time steps. In the standard model, at each time step a specific vertex must be included in the dominating set. In the eviction model, a specific vertex must no longer be in the dominating set. In each case, the reconfiguration step involves some vertices in the current dominating set being replaced by neighbours, and the minimum number of vertices which allow for a dominating set to be dynamically maintained “forever” is the {\it eternal domination number} of the graph. We discuss algorithmic and complexity issues regarding the eternal domination number, and bounds for the eternal domination number in terms of other graph parameters. We then consider the sequence of eternal domination numbers obtained by allowing at most $1,, 2, \ldots$ vertices to be replaced in each reconfiguration step. Lastly, we consider the situation where more than one specific vertex must be included in the new dominating set. A variety of open problems will be raised.
Title: Monochromatic connectivity of graphs
Abstract:
An edge-coloured path is monochromatic if all of its edges have the same colour. For a k-connected graph G, the monochromatic k-connection number of G, denoted by mc_k(G), is the maximum number of colours in an edge-colouring of G such that, any two vertices are connected by k internally vertex-disjoint monochromatic paths. In this paper, we shall study the parameter mc_k(G). We obtain bounds for mc_k(G), for general graphs G. We also compute mc_k(G) exactly when k is small, and G is a graph on n vertices, with a spanning k-connected subgraph having the minimum possible number of edges, namely \lceil\frac{kn}{2}\rceil. This is based on joint work with Qingqiong Cai, Shinya Fujita, and Henry Liu.
Last Update: 21 March. 2024