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Every edge is in a red ellipse (the bags). The bags are connected in a tree. The bags an original vertex is part of are connected.
Directed Weighted w3 w1 w2 w5 w9 w11 w8 w10 w7 w6 w4
Recursively build paths: O(n k ) Can there be algorithms with runtimes on the form f(k)n O(1) ? … and if so, how small can f(k) be?
Consider regular graphs of degree d: Either d>k: There must be k-path. Or d<=k: We can list all potential k-paths in nd k <=nk k time.
<k? B1 B2 B3 B4 B5 B6 Depth First Search
B1B2B3 B4 B5 B6
13 5 246 Prob[rainbow k-path] >= k!/k k ~ e -k
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Minimum Spanning Trees. Subgraph A graph G is a subgraph of graph H if –The vertices of G are a subset of the vertices of H, and –The edges of G are a.
Chapter 15 Graph Theory © 2008 Pearson Addison-Wesley. All rights reserved.
Eulerian Tour What is a Eulerian tour and how to find one.
Search Related Algorithms. Graph Code Adjacency List Representation:
COSC 2007 Data Structures II Chapter 14 Graphs III.
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