Latest posts tagged with #OrientedGraph on Bluesky
Day 20 of #SSNC facts! We're examining how standard #algorithms handle the #SeymourConjecture's. Remember, this #Conjecture seeks an #OrientedGraph whose second neighborhood is at least as large as its first. We last looked at Dijkstra. Today, Bellman-Ford. #ComputerScience #Math
Day 18 of #SSNC facts! We're looking at the #SeymourConjecture: Does every #OrientedGraph have a node with a second neighborhood at least as large as its first? Can traditional #GraphTheory #Algorithms solve the neighborhood size challenge? Today, we examine #DepthFirstSearch (DFS). #Math
Let's illustrate: Consider this #OrientedGraph: x->y->z, y->w, z->w. BFS assigns levels correctly, but the back arc (z->w) creates a path that distorts the second neighborhood of 'y' for #SSNC analysis. Back arcs are a problem for the #SeymourConjecture and must be handled.
Day 17 of #SSNC facts! Remember, we're exploring: Does every #OrientedGraph have a node with a second neighborhood at least as large as its first? Why is this deceptively simple question still unsolved? #GraphTheory #Resesrch #Math #ComputerScience #SeymourConjecture
Day 16 of #SSNC facts! We've been discussing the #SeymourConjecture: It asks the questionv Does every #OrientedGraph have a node whose second neighborhood is at least as large as its first? Open since 1990, but why is this still unsolved? Let's explore.
#GraphTheory #Math #ComputerScience
#Challenge! 🧠 Given the attached #OrientedGraph, what node order maximizes the number of forward edges? (Median Order!) Havet & Thomassé used this concept in their work. Show your solution! #GraphTheory #MedianOrder #Algorithms #TournamentTheory #DeanConjecture #SeymourConjecture #math #mathematics
#ProgrammingChallenge: What's the best data structure for storing a #graph? #OrientedGraph? #Tournament? Discuss #AdjacencyMatrices, #Lists, #EdgeLists, etc. Pros & cons? #GraphTheory #DataStructures #SSNC
Day 6 of #SSNC facts! Now that we've covered the basic definitions, let's talk about why the #SeymourConjecture (which asks if an #OrientedGraph has a node whose second neighborhood is at least as large as the first). #math #GraphTheory #ComputerScience
Here's a #programming question. How could we distinguish between a node's first and second neighbor's in an #OrientedGraph? What problems could arise? #SeymourConjecture #GraphTheory #Developers #dev #TCS #Coding #computerscience
The #SeymourConjecture states that there exists a vertex in an #OrientedGraph has at least as many vertices in its first second out-neighborhood as in its first out-neighborhood. This Conjecture has remained open since 1990. #OpenProblem #SSNC #GraphTheory #math #mathematics #mathsky #compsky
Day 5 of #SSNC facts! The conjecture asks there exists a vertex in an #OrientedGraph that has at least as many vertices in its second out-neighborhood as in its first out-neighborhood. #math #SeymourConjecture #GraphTheory
The scope of #KnowledgeGraphs is vast, practically limitless! This means any domain with a glossary and defined relationships can be represented as an #OrientedGraph. Think about how many fields could benefit from this structured knowledge representation! #DataScience #AI #InformationRetrieval.
This one is for the #developers and #programmers! How would you verify if a given directed graph is oriented (no 2-cycles)? Or, how would you generate a random #OrientedGraph of a given size? There is a lot of coding in #GraphTheory! #Coding #Algorithms #Math #SeymourConjecture #SSNC #TCS
The #SeymourConjecture asks if in any #OrientedGraph (a directed graph without two-way edges between any pair of nodes), is there always at least one node whose second neighborhood is at least as large as its first neighborhood? #SSNC #GraphTheory #math
The node 0 is the node under consideration. It's first neighborhood is in light blue and it's second neighborhood is in the green.
Day 2 of the #SSNC facts! The #SeymourConjecture has been a major open problem in #GraphTheory for decades. It asks an important question about the relationship between a node's first and second neighborhoods in an #OrientedGraph. #math
