C. Valqui

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20072025

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math.CO2021

Minimal graph in which the intersection of two longest paths is not a separator

Juan Gutiérrez, Christian Valqui

We prove that for a connected simple graph $G$ with $n \leq 10$ vertices, and two longest paths $C$ and $D$ in $G$ , the intersection of vertex sets $V (C) \cap V (D)$ is a separator. Th…

math.CO2021

Bi-traceable graphs, the intersection of three longest paths and Hippchen's conjecture

Juan Gutiérrez, Christian Valqui

Let $P, Q$ be longest paths in a simple graph. We analyze the possible connections between the components of $P \cup Q ∖ (V (P) \cap V (Q))$ and introduce the notion of a bi-trac…