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Combinatorial optimization typically deals with optimizing over a finite set of objects that have some combinatorial structure (e.g. trees, matchings, matroids). Approximation algorithms, polyhedral methods, and integer programming are all on topic.
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 …
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 …