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Results tagged with co.combinatorics
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user 1028
Enumerative combinatorics, graph theory, order theory, posets, matroids, designs and other discrete structures. It also includes algebraic, analytic and probabilistic combinatorics.
3
votes
Hamilton cycle decompositions of the complete graph
In Two-factorizations of complete graphs it is stated that $K_9$ has 122 non-isomorphic Hamiltonian decompositions, and the corresponding number for $K_{11}$ is 3140 (EDIT: the actual figure is much m …
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13
votes
2
answers
402
views
Regularizing graphs
Let $G$ be a simple graph (undirected, no loops or parallel edges), with maximum degree $\Delta(G)$. I would like to add edges to the graph to make it regular, without increasing the maximum degree.
…
- 726
21
votes
8
answers
8k
views
Why is edge-coloring less interesting than vertex-coloring?
I was wondering why there is (apparently) much more research directed towards vertex-coloring than edge-coloring? Prima facie, it seems that edge-coloring is just as "natural" a thing to investigate.
…
21
votes
Accepted
What is the Tutte polynomial encoding?
No-one so far has mentioned matroids. The Tutte polynomial encodes some of the information from the cycle matroid of the graph. Two graphs with the same cycle matroid (and number of vertices) have the …
- 726
1
vote
3
answers
515
views
Finding maximum value of degree-3 homogeneous polynomials when variables sum to 1
I would like to be able to find maximum values of degree-3 homogeneous polynomials, when the variables are non-negative real numbers that sum to 1. For example,
For example, the maximum value of $xy^ …
- 726