Cappello, Chiara: Critically frustrated signed graphs : by Chiara Cappello ; Advisor: Prof. Dr. Eckhard Steffen. Paderborn, 2023
Inhalt
- List of Figures
- Introduction
- Critically frustrated signed graphs
- Characterization and families of critical signed graphs
- Decomposition and subdivision of critical signed graphs
- Characterization of 1- and 2-critical signed graphs
- The family of critically 3-frustrated planar signed graphs
- The families L and L*
- Infinite families of k-critical signed graphs
- Construction for non-decomposable critically frustrated signed graphs
- The family L*
- -K5-minor-free signed graphs
- Finiteness of L*(3)
- Preliminaries
- Proof of Theorem 4.0.1
- Structural properties of (, )
- Proof of Proposition 4.2.1
- Proof of Proposition 4.2.2
- Proof of Proposition 4.2.3
- Proof of Proposition 4.2.4
- The families S and S*
- Signed graph coloring
- The symset t-chromatic number
- Brooks' type theorem for the symset t-chromatic number
- Symset t-chromatic spectrum
- The t-chromatic polynomial
- The symset chromatic number
- Conclusion and future work