: We present an improved upper bound of O(d1+ 1 m−1 ) for the (2, F)-subgraph chromatic number χ2,F (G) of any graph G of maximum degree d. Here, m denotes the minimum number of...
Upper and lower bounds are obtained for the joint entropy of a collection of random variables in terms of an arbitrary collection of subset joint entropies. These inequalities gene...
For a connected graph G, let L(G) denote the maximum number of leaves in a spanning tree in G. The problem of computing L(G) is known to be NP-hard even for cubic graphs. We improv...
We consider exploration problems where a robot has to construct a complete map of an unknown environment. We assume that the environment is modeled by a directed, strongly connecte...
A secret-sharing scheme realizes a graph if every two vertices connected by an edge can reconstruct the secret while every independent set in the graph does not get any informatio...