A note on two problems in connexion with graphs

A vertex subset S of graph G is a total dominating set of G if every vertex of G is adjacent to a vertex in S. For a graph G with no isolated vertex, the total domination number of G, denoted by @c"t(G), is the minimum cardinality of a total dominating ...

The Hadwiger number of a graph G, denoted h ( G ), is the largest integer t such that G contains K t as a minor. A famous conjecture due to Hadwiger in 1943 states that for every graph G, h ( G ) ≥ χ ( G ), where χ ( G ) denotes the ...

A vertex subset of a graph is a dominating set if every vertex of the graph belongs to the set or has a neighbor in it. A connected dominating set is a dominating set such that the induced subgraph of the set is a connected graph. A graph is called ...