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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.

0 votes

In what types of graphs can the maximum independent set be found in polynomial time?

Considering your graphs seem to be defined sequentially (for numbers $N$ in $[2,15]$), if your graphs are constructed in a way that the graph at $N$ can be constructed from operations that duplicate ( …
JimN's user avatar
  • 265
1 vote

Automated search for bijective proofs

Does the OEIS count? Three of your papers are listed in https://oeis.org/wiki/Works_Citing_OEIS as having used the help of either OEIS or Superseeker , I presume to help find a (potential?) bijection. …
JimN's user avatar
  • 265
2 votes

Relaxing Meyniel graphs: condition for strongly perfect instead of very strongly perfect

You ask: Does this mean every induced subgraph of G which are cycles of odd length at least 5 has at least 2 chords? No, that doesn't make sense. If an induced subgraph is an induced cycle, then it …
JimN's user avatar
  • 265
0 votes

maximal sets of vertices that avoids a clique

Given the fixed $k$, you could look at all $\binom{n}{k}$ subsets of vertices to see if they form a clique of size $k$ (or do whatever you like to enumerate all cliques of size $k$ -- there might be a …
JimN's user avatar
  • 265
1 vote

Relationship between cycle length, number of chords, and number of induced $P_{4}$ subgraphs...

I agree with Cycle of length 5 with 0 chords: Number of P4 induced subgraphs: 5 Cycle of length 5 with 1 chord: Number of P4 induced subgraphs: 2 But I'm not sure how to interpret your statement: C …
JimN's user avatar
  • 265
4 votes

Combinatorial databases

The Combinatorial Object Server (CoS) can generate perms/combs, sets/multisets, partitions, DeBuijn seqs/Lyndon words/necklaces, graphs, and a few others, all through a web interface. Unfortunately, i …