Mar 5, 2025 · A minimum spanning tree (MST) or minimum weight spanning tree for a weighted, connected, and undirected graph is a spanning tree (no cycles and connects all vertices) that has minimum weight. The weight of a spanning tree is the sum of all edges in the tree. In Kruskal’s algorithm, we sort all edges of the given graph in increasing order.

From here, you can use DFS and BFS to find the maximum weight edge (u, v) on the cycle, and return the edge set of G - (u, v) that represents the MST. An MST of a graph with distinct weights will never include the max weight edge of a cycle.

Feb 15, 2015 · I have the following algorithm: For a given (finite undirected simple) graph G=(V,E) with positive weight function on the edges: Run DFS (depth-first-search) till you find an edge going backwards or DFS stopped.

Dec 26, 2014 · I'm trying to implement an algorithm in c which finds MST using DFS. I've already found the DFS algortihm and i understand it pretty well. I also know that i should follow these steps to achieve my purpose :

Kruskal’s algorithm is another algorithm for finding a minimum spanning tree (MST) in a graph. Kruskal’s algorithm has just a few simple steps: Given a list of the edges in a graph, sort the list of edges by their edge weights. Build up a minimum spanning tree by considering each edge from least weight to greatest weight.

Oct 9, 2020 · Starting from vertex a, there are two possible results to depth-first search: a->b->c->d->e->f->g->h, and a->h->g->f->e->d->c->b. The former returns a very long path from a to h, and the latter returns a very long path from a to b. Note that in this example, the graph is undirected.

Feb 24, 2025 · This article provides a theoretical explanation of Depth-First Search (DFS), Breadth-First Search (BFS), and Minimum Spanning Tree (MST) algorithms, along with their applications and basic...

This report dives into key algorithms used for solving problems in weighted graphs, including techniques to find Minimum Spanning Trees (MST), traverse graphs, and calculate shortest paths in directed graphs.

Every DFS-tree of a complete graph is a path, no matter how you order the edges. But clearly you can define the weights such that a non-path is the MST. See the example below (MST in red).

Feb 26, 2025 · Prim’s algorithm is guaranteed to find the MST in a connected, weighted graph. It has a time complexity of O ( (E+V)*log (V)) using a binary heap or Fibonacci heap, where E is the number of edges and V is the number of vertices. It is a relatively simple algorithm to understand and implement compared to some other MST algorithms. Disadvantages: