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Decision - Bipartite graphs
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Terms in this set (10)
Bipartite graph
A graph to show which vertices in one set can be matched to which vertices in the other set.
Partial matching
Some of the vertices in the bipartite graph are cannot be linked to a vertex in the other set because the vertices it can link to are already in use.
Set
There are two groups of vertices, one on each side of the graph. Each group is called a _____. There are no links between vertices in the same group.
Maximal matching
As many vertices as possible are matched. Sometimes it is impossible for all vertices in a bipartite graph to be matched (this is called a complete matching).
A4, B1, C3, D2
A bipartite graph has the following edges: A1, A4, B1, B2, C1, C3, C4, and D2. List the edges that give the only possible complete matching for this graph.
9
A bipartite graph has 6 vertices with degree 6 in one set. How many vertices must be in the other set if each one has a degree of 4?
11
How many edges are in the maximal matching for a bipartite graph with 11 vertices in one set and 15 in the other, given that there are 160 edges in the set?
12
A bipartite graph has 8 vertices. Each vertex is connected to 3 vertices in the other set. Given that a complete matching is possible, state the number of edges in the graph.
15
A bipartite graph has 5 vertices in each set. There is only one possible maximal matching. What is the maximum possible number of vertices?
16
A bipartite graph has 64 edges. What is the minimum number of vertices it must have?
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