César Hernández-Cruz

activity

20162026

most citedMinimal digraph obstructions for small matrices

2 citations · 3 across the 11 of their papers we have counts for

collaborators

11 papers

math.CO2026

Full homomorphisms to graph classes

Pavol Hell, César Hernández-Cruz

Given a family of graphs $F$ , we define a graph $G$ to be fully $F$ -colourable if $G$ admits a full homomorphism to some $F$ in $F$ . We approach the p…

math.CO2025

Strong chordality in tournaments and multipartite tournaments with possible loops

Pavol Hell, César Hernández-Cruz, Jing Huang

Strongly chordal digraphs are included in the class of chordal digraphs and generalize strongly chordal graphs and chordal bipartite graphs. They are the digraphs that admit a line…

math.CO2022

Minimal obstructions for polarity, monopolarity, unipolarity and $(s, 1)$ -polarity in generalizations of cographs

Fernando Esteban Contreras-Mendoza, César Hernández-Cruz

It is known that every hereditary property can be characterized by finitely many minimal obstructions when restricted to either the class of cographs or the class of $P_{4}$ -reducibl…

math.CO2021

Describing hereditary properties by forbidden circular orderings

Santiago Guzmán-Pro, Pavol Hell, César Hernández-Cruz

Each hereditary property can be characterized by its set of minimal obstructions; these sets are often unknown, or known but infinite. By allowing extra structure it is sometimes p…

math.CO2021★ 1 cited

Minimal obstructions to $(\infty, k)$ -polarity in cographs

F. Esteban Contreras-Mendoza, César Hernández-Cruz

A graph is a cograph if it does not contain a 4-vertex path as an induced subgraph. An $(s, k)$ -polar partition of a graph $G$ is a partition $(A, B)$ of its vertex set such that $…

math.CO2020

Oriented expressions of graph properties

Santiago Guzmán-Pro, César Hernández-Cruz

Several graph properties are characterized as the class of graphs that admit an orientation avoiding finitely many oriented structures. For instance, if $F_{k}$ is the set of homomor…

math.CO2020

Minimal obstructions for a matrix partition problem in chordal graphs

Juan Carlos García-Altamirano, César Hernández-Cruz

If $M$ is an $m \times m$ matrix over ${0, 1, *}$ , an $M$ -partition of a graph $G$ is a partition $(V_{1}, \dots V_{m})$ such that $V_{i}$ is completely adjacent (non-adjacent) to…

math.CO2020

Duality pairs and homomorphisms to oriented and unoriented cycles

Santiago Guzmán-Pro, César Hernández-Cruz

In the homomorphism order of digraphs, a duality pair is an ordered pair of digraphs $(G, H)$ such that for any digraph, $D$ , $G \to D$ if and only if $D \neq \to H$ . The directed path…

math.CO2019

Panchromatic patterns by paths

Germán Benítez-Bobadilla, Hortensia Galeana-Sánchez, César Hernández-Cruz

Let $H = (V_{H}, A_{H})$ be a digraph, possibly with loops, and let $D = (V_{D}, A_{D})$ be a loopless multidigraph with a colouring of its arcs $c : A_{D} \to V_{H}$ . An $H$ -path of $D$ is…

math.CO2017

A characterization of trees having a minimum vertex cover which is also a minimum total dominating set

César Hernández-Cruz, Magdalena Lemańska, Rita Zuazua

A vertex cover of a graph $G = (V, E)$ is a set $X \subseteq V$ such that each edge of $G$ is incident to at least one vertex of $X$ . A dominating set $D \subseteq V$ is a total do…

math.CO2016★ 2 cited

Minimal digraph obstructions for small matrices

Pavol Hell, César Hernández-Cruz

Given a ${0, 1, *}$ -matrix $M$ , a minimal $M$ -obstruction is a digraph $D$ such that $D$ is not $M$ -partitionable, but every proper induced subdigraph of $D$ is. In this not…

Full homomorphisms to graph classes

Strong chordality in tournaments and multipartite tournaments with possible loops

Minimal obstructions for polarity, monopolarity, unipolarity and (s,1)-polarity in generalizations of cographs

Describing hereditary properties by forbidden circular orderings

Minimal obstructions to (∞,k)-polarity in cographs

Oriented expressions of graph properties

Minimal obstructions for a matrix partition problem in chordal graphs

Duality pairs and homomorphisms to oriented and unoriented cycles

Panchromatic patterns by paths

A characterization of trees having a minimum vertex cover which is also a minimum total dominating set

Minimal digraph obstructions for small matrices

Minimal obstructions for polarity, monopolarity, unipolarity and $(s, 1)$ -polarity in generalizations of cographs

Minimal obstructions to $(\infty, k)$ -polarity in cographs