Latest posts tagged with #OrientedGraphs on Bluesky
Arc-Density Lower Bound for Pushably 3‑Critical Oriented Graphs
Any pushably 3‑critical oriented graph on n vertices needs at least (15n + 2)⁄13 arcs. If a graph’s max average degree < 30⁄13 and girth ≥5, its pushable chromatic number ≤3. getnews.me/arc-density-lower-bound-... #pushablecolours #orientedgraphs
#SeymourConjecture: In its standard form, #Dijkstra's algorithm is ill-equipped to address the #SSNC's core challenge: analyzing the size of 1st & 2nd neighborhoods in #OrientedGraphs. What modifications could make it more relevant? #TCS #ComputerScience
Yesterday we explored BFS: a general traversal #algorithm, not a #SeymourConjecture solver. It's designed for level-order exploration, not neighborhood analysis. This means it doesn't inherently handle back arcs, leading to potential misrepresentations of neighborhoods in #OrientedGraphs. #math
#CodingChallenge: How would you implement BFS? What special considerations arise when working with #OrientedGraphs? Would allowing bi-directed edges (directed graphs) simplify or complicate your code? And what #DataStructure would you choose? Let's discuss! #developers #dev #programming #coding
Day 9 of #SSNC facts! Let's explore #tournaments. These are complete #OrientedGraphs. Every node pair has exactly one directed edge. The #DeanLatkaConjecture asks: is there always a node with a second neighborhood at least as large as its first? #GraphTheory #Math #research
This is just a simple statement But it's also a decades-long puzzle? Is the #SeymourConjecture like an unbeatable video game challenge? What hidden complexity lies in these #OrientedGraphs? #MathProblems #Unsolved #GraphTheory #OpenProblems
In these fields that can be represented by #OrientedGraphs (transportation, social media, #KnowledgeGraphs and more), a solution to the #SeymourConjecture helps is locate the "influencers", the ones who being are talked about. #math #GraphTheory #ComputerScience
A #KnowledgeGraph represents a network of entities (people, places, things) and their relationships. These (directional) relationships, allow machines to understand complex information networks. They can generally be modeled using #OrientedGraphs! #GraphTheory #Math #Mathematics
Day 4 of #SSNC facts! Before diving back into #SeymourConjecture, let's appreciate the power of #OrientedGraphs. I want to say they're literally ALL around us. They have a crucial role in representing knowledge. Let's talk #KnowledgeGraphs! #GraphTheory #Math #Mathematics
#OrientedGraphs aren't just #math though! They model real-world scenarios: project management (dependencies), communication networks (information flow), biological systems (predator-prey), transportation (one-way streets), social media (directed relationships). #GraphTheory #SeymourConjecture #SSNC
Day 3 of SSNC facts! Why does the #SeymourConhecture focus on #OrientedGraphs? I don't know Seymour's initial intent. But oriented graphs don't have bidirectional edges, so they're closer in structure to undirected graphs than directed graphs. They offer a stepping stone! #graphTheory #SSNC #Math
