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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.
15
votes
Combinatorial databases
Not related to polyominos, but I like House of Graphs: https://houseofgraphs.org
It allows you to search by graph6 code, so if you find an interesting graph, you can check whether that graph has arise …
5
votes
Accepted
List chromatic index of a particular graph
Greedy coloring works here to show $2p$-choosability, I believe, and the hypothesis that $p$ is prime doesn't appear to be necessary. Write the cliques as $A = \{a_1, \ldots, a_{p+1}\}$ and $B = \{b_1 …
12
votes
Accepted
Blinking graphs
This question seems quite similar to the problem of parity domination. Let $S$ be the set of vertices with label $1$. The condition that $S$ flips to its complement after updating is equivalent to the …
8
votes
Accepted
How many uniquely colored degree two vertices in 3-coloring of subcubic graph?
No such graph exists (that is, you cannot have a subcubic graph with three degree-$2$ vertices all forced to the same color). Suppose that such a graph exists; we may assume the graph is connected. Th …
9
votes
Accepted
What is the correct statement of this Erdös-Gallai-Tuza problem generalizing Turan's triangl...
I hope I am not violating any kind of MathOverflow etiquette by responding to a question 2 years after it has been asked, but your question is answered in the following preprint of mine that just hit …