P1 & P2 Path Partition: Same End Vertices Possible?

  • Context: Undergrad 
  • Thread starter Thread starter kimkibun
  • Start date Start date
  • Tags Tags
    Partition Path
Click For Summary
SUMMARY

The discussion centers on the possibility of two path partitions, P1 and P2, in a graph having the same end vertices. It is established that while path partitions are defined as vertex-disjoint, there are exceptions, such as cycles, where P1 and P2 can indeed share the same end vertices. This highlights a nuanced understanding of graph theory definitions and their implications in specific scenarios.

PREREQUISITES
  • Understanding of graph theory concepts, specifically path partitions
  • Familiarity with vertex-disjoint definitions in graph structures
  • Knowledge of cycles in graph theory
  • Basic comprehension of mathematical proofs and counterexamples
NEXT STEPS
  • Research the properties of vertex-disjoint paths in graph theory
  • Explore the implications of cycles in path partitions
  • Study examples of graph partitions and their definitions
  • Learn about advanced graph theory concepts such as Eulerian and Hamiltonian paths
USEFUL FOR

Graph theorists, computer scientists, mathematicians, and students studying advanced graph algorithms and their properties.

kimkibun
Messages
28
Reaction score
1
sorry if i posted this topic here..let P1 and P2 be a path partition of a graph.is it possible that P1 and P2 to have the same end vertices?
 
Physics news on Phys.org
Yes, for example a some cycle.
 
but sir, according to the definition of path partition, it should be vertex-disjoint..
 

Similar threads

Undergrad Finding vertex of a 3D Triangle on a Plane
  • · Replies 3 ·
Replies
3
Views
2K
Graduate Interpreting photon correlations from independent sources
  • · Replies 178 ·
6
Replies
178
Views
9K
Undergrad Why work is PdV and not (P+dP)dV in an isothermal process?
  • · Replies 6 ·
Replies
6
Views
604
Graduate Calculate the work done by pressure rupturing a spherical containment
  • · Replies 7 ·
Replies
7
Views
2K
Undergrad Can ambiguity in the word "measurement" allow contradictions in QM?
  • · Replies 5 ·
Replies
5
Views
1K
Graduate Geometry: problem with defining the vertices of a tunnel around a given path
  • · Replies 1 ·
Replies
1
Views
3K
Finding the pressure of a gas in three identical balloons
  • · Replies 12 ·
Replies
12
Views
2K
Undergrad How can I prove that P2 = density* g H
  • · Replies 38 ·
2
Replies
38
Views
6K
Undergrad Understanding part of the multinomial formula
  • · Replies 3 ·
Replies
3
Views
2K
High School Do Entangled Photons React to possible Photon-Photon Collisions?
  • · Replies 4 ·
Replies
4
Views
2K