Every tree is bipartite.    [1] Every graph contains a spann…

Every tree is bipartite.    [1] Every graph contains a spanning tree as a subgraph. [2] If a graph has exactly one more vertex than it has edges, then the graph is a tree. [3] Every forest is a tree. [4] Every connected graph contains a spanning tree as a subgraph. [5] If a graph has two more vertices than edges, then it is not connected. [6]

Given a graph, it is possible to find more than one spanning…

Given a graph, it is possible to find more than one spanning tree [st] A spanning tree with the smallest possible comgined weight is called a [mst] We often designate a particular vertex in a tree so that every other vertex on the tree can be characterized by its position relative to this particular vertex which is called the [rt] Given a graph, there can be at most one Hamilton path [hp]