2 research outputs found
Gluing Associated Prime Ideals of Small Height
Let be a local (Noetherian) ring and suppose that has associated
prime ideals where . We identify sufficient conditions for there to
exist a local (Noetherian) subring of such that and have the
same completion and has exactly associated prime ideals. We include
applications and consequences of this result.Comment: 14 page
Bounds on higher graph gonality
We prove new lower and upper bounds on the higher gonalities of finite
graphs. These bounds are generalizations of known upper and lower bounds for
first gonality to higher gonalities, including upper bounds on gonality
involving independence number, and lower bounds on gonality by scramble number.
We apply our bounds to study the computational complexity of computing higher
gonalities, proving that it is NP-hard to compute the second gonality of a
graph when restricting to multiplicity-free divisors.Comment: 14 pages, 5 figure