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Enumerative combinatorics, graph theory, order theory, posets, matroids, designs and other discrete structures. It also includes algebraic, analytic and probabilistic combinatorics.

4 votes
1 answer
844 views

New edge coloring problem in graph theory

Let $G$ be a simple graph. Consider the following edge coloring: We are allowed to use repetitive colors on some edges incident to a vertex such that the result does not contain a sequence of length …
2 votes
0 answers
284 views

Does this idea give an algorithm for constructing Hadamard matrices?

Fedor Petrov's answer of my preceding question shows that my question reduces to the famous Hadamard conjecture about Hadamard matrices of order $4k$. So I decided to study this conjecture and I got …
1 vote
1 answer
152 views

Edges of every simple graph can be colored with at most $s+1$ color

This question is related to my previous post: New edge coloring problem in graph theory. Added: Let $G$ be a simple graph. Consider the following edge coloring: We are allowed to use repetitive co …