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Results tagged with Search options answers only user 19
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Questions about properties of and problems on graphs, discrete data structures that have the form of nodes connected by edges, that is networks.

You must remember that the vertices diagonal from one another can be colored the same! Your formula does not take that into account. We can find the chromatic number of a graph via the inclusion-exclu …
answered Sep 27 '12 by Nicholas Mancuso
For clarity let $T= (V,E)$ be a tournament and let $a \rightsquigarrow b$ denote a path from $a$ to $b$ in $T$. A simple directed cycle clearly gives a tournament with more than one ranking. Suppose …
answered Mar 10 '13 by Nicholas Mancuso
Given a bipartite graph $G = (U,V,E)$ and a maximum matching $M$ of $G$, via Konig's Theorem we see that $|M| = |C|$ where $C$ is a minimum vertex cover for $G$. Your statement is merely an upper boun …
answered Sep 22 '12 by Nicholas Mancuso
You wish to find the minimal set of ($s$-$t$)-paths such that each edge is covered. I believe this problem is very similar to the chinese postman problem. First, add a directed edge from $t$ to $s$ to …
answered May 8 '12 by Nicholas Mancuso
As I stated on the CSTheory post, this is solved via maximum matching. The following should give enough intuition to show that each agent $a_i$ has a $q_i$-matching iff a transformed graph $G'$ has a …
answered Sep 22 '12 by Nicholas Mancuso
All-Pairs-Shortest Path Given a graph $G = (V, E)$ find the shortest path between any two nodes $u,v \in V$. It can be solved by Floyd-Warshall's Algorithm in time $O(|V|^3).$ Many believe the APSP p …
answered Sep 20 '12 by Nicholas Mancuso
Let $P$ be the set of people and $\mathcal{S}$ be the modified multi-set of subsets. By checking if an $\mathcal{S}$-saturated matching into $P$ exists (i.e. Hall's condition) you are indeed finding a …
answered Mar 18 '13 by Nicholas Mancuso
To expand upon my comment, remember, this algorithm for finding Min-Cost-Flow relies on the fact that $f$ is maximal. By first running Ford-Fulkerson to find $f$ and the resulting residual network \$G_ …
answered Nov 20 '12 by Nicholas Mancuso
You shouldn't need to keep track of state. This can all be handled with capacity constraints over the nodes. The network can be structured as follows: Start with the graph where one partition consist …
answered Nov 27 '14 by Nicholas Mancuso
If the edges in the graph only represent valid moves between certain positions, using Dijkstra's would work just fine. However as the graph is unweighted it would be overkill. A simple breadth-first-s …
answered Apr 18 '12 by Nicholas Mancuso