Edge Colouring of Bipartite Graphs: Proving Valency Equality

  • Thread starter Thread starter Stephane G
  • Start date Start date
  • Tags Tags
    Edge Graphs
AI Thread Summary
The discussion centers on proving by induction that the edge coloring number of any bipartite graph equals its maximum valency. Participants emphasize the importance of showing initial work and thought processes before seeking help, as the problem resembles a homework assignment. There is a request for ideas and previous attempts related to the problem. Additionally, the task includes finding an edge coloring for a specific bipartite 4-regular graph derived from 2-regular graphs. Engaging with the problem collaboratively is encouraged to enhance understanding.
Stephane G
Messages
2
Reaction score
0
Prove by induction on the number of edges in a graph that any bipartite graph has edge colouring number equal to its maximum valency. Also, Find such an edge colouring for a bipartite 4-regular cartesian or tensor product of your choice of 2-regular graphs
 
Mathematics news on Phys.org
Stephane G said:
Prove by induction on the number of edges in a graph that any bipartite graph has edge colouring number equal to its maximum valency. Also, Find such an edge colouring for a bipartite 4-regular cartesian or tensor product of your choice of 2-regular graphs

Hey Stephane G and welcome to the forums.

For these kinds of questions, we ask that you show any working and any of your thinking before we help with these kinds of problems, since it is in the form of a homework problem (note it doesn't have to be a homework problem, just in the format of one).

What ideas do you have? What have you tried before?
 

Thread 'What Exactly is Dirac’s Delta Function? - Insight'

Insights auto threads is broken atm, so I'm manually creating these for new Insight articles. In Dirac’s Principles of Quantum Mechanics published in 1930 he introduced a “convenient notation” he referred to as a “delta function” which he treated as a continuum analog to the discrete Kronecker delta. The Kronecker delta is simply the indexed components of the identity operator in matrix algebra Source: https://www.physicsforums.com/insights/what-exactly-is-diracs-delta-function/ by...
View full post »

Thread 'Non-orthogonal bases'

Suppose ,instead of the usual x,y coordinate system with an I basis vector along the x -axis and a corresponding j basis vector along the y-axis we instead have a different pair of basis vectors ,call them e and f along their respective axes. I have seen that this is an important subject in maths My question is what physical applications does such a model apply to? I am asking here because I have devoted quite a lot of time in the past to understanding convectors and the dual...
View full post »
Thread 'Imaginary Pythagoras'

Thread 'Imaginary Pythagoras'

I posted this in the Lame Math thread, but it's got me thinking. Is there any validity to this? Or is it really just a mathematical trick? Naively, I see that i2 + plus 12 does equal zero2. But does this have a meaning? I know one can treat the imaginary number line as just another axis like the reals, but does that mean this does represent a triangle in the complex plane with a hypotenuse of length zero? Ibix offered a rendering of the diagram using what I assume is matrix* notation...
View full post »

Similar threads

B 4-colours theorem can be proved visually
Replies
21
Views
2K
Counting edge numbers in bipartite graphs
Replies
1
Views
1K
B Can you read my English on 4 colour theorem?
Replies
8
Views
2K
I Edge connectivity of a graph given the number of edge disjoint paths
Replies
1
Views
1K
I Prove that a given graph contains a cycle using induction (Graph Theory)
Replies
7
Views
3K
I The number of intersection graphs of ##n## convex sets in the plane
Replies
2
Views
1K
I A way to comprehend the geometry of a hypercube
Replies
2
Views
2K
MHB How many new branches will the complement graph of a deleted edge have?
Replies
11
Views
2K
I Number of edges in a tree digraph
Replies
5
Views
2K
How to prove that 2 graphs are not isomorphic?
Replies
4
Views
11K

Hot Threads

Recent Insights

Back
Top