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Questions about graphs, discrete structures of nodes which are connected by edges, including trees and graphs with weighted edges.

4 votes
1 answer
173 views

Disproving well-quasi-order by providing an infinite anti-chain

More specifically, I've been trying to solve an exercise from the following lecture which asks whether the class of $P_{3}\text{-free}$ graphs is a w.q.o or not on the induced subgraph operation $\leq … \rbrace$ with $G_{i}$ representing all $P_{3}\text{-free}$ graphs on $i$ vertices (and graphs in $G_{i}$ being represented in a touple-like alpharithmetic form $(a_{1},....,a_{i})$ such that $a_{1 …
jjohn's user avatar
  • 474
-1 votes
1 answer
144 views

Minimising two maximum edges in s-t path

I've been trying to solve the following problem: Problem is the following: Given a graph and a pair of nodes $s$, $t$ you have to find the path from $s$ to $t$ which minimises the sum of its two …
jjohn's user avatar
  • 474
2 votes

Algorithm for grid with obstacles and movement restriction

You can depict states of the graph as following: (grid_position,|consecutive_left|,|consecutive_up|) if you are at state ([2,3],3,0) then you have no other option but to go up to ([3,3],0,1) so you …
jjohn's user avatar
  • 474
7 votes

How to solve an arrangement problem at the Archive Nationale of France using graph theory?

I think I have a solution to your problem. Hopefully I haven't misunderstood something in the definition of your problem. Here it goes: I'm going to describe a Dynamic Programming approach. It's an …
jjohn's user avatar
  • 474
4 votes
1 answer
520 views

Maximum bipartite matching with extra reward for covering certain sets

Consider the following variation of Bipartite Maximum Matching. As usual, we have a bipartite graph $G$. In addition, there is an additional collection of sets $S_1,S_2,\dots,S_k$, with each set $S …
jjohn's user avatar
  • 474