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About uniquely colorable mixed hypertrees

Angela Niculitsa; Vitaly Voloshin — 2000

Discussiones Mathematicae Graph Theory

A mixed hypergraph is a triple 𝓗 = (X,𝓒,𝓓) where X is the vertex set and each of 𝓒, 𝓓 is a family of subsets of X, the 𝓒-edges and 𝓓-edges, respectively. A k-coloring of 𝓗 is a mapping c: X → [k] such that each 𝓒-edge has two vertices with the same color and each 𝓓-edge has two vertices with distinct colors. 𝓗 = (X,𝓒,𝓓) is called a mixed hypertree if there exists a tree T = (X,𝓔) such that every 𝓓-edge and every 𝓒-edge induces a subtree of T. A mixed hypergraph 𝓗 is called uniquely...

Color-bounded hypergraphs, V: host graphs and subdivisions

Csilla Bujtás; Zsolt Tuza; Vitaly Voloshin — 2011

Discussiones Mathematicae Graph Theory

A color-bounded hypergraph is a hypergraph (set system) with vertex set X and edge set = E₁,...,Eₘ, together with integers $s_{i}$ and $t_{i}$ satisfying $1 \leq s_{i} \leq t_{i} \leq | E_{i} |$ for each i = 1,...,m. A vertex coloring φ is proper if for every i, the number of colors occurring in edge $E_{i}$ satisfies $s_{i} \leq | φ (E_{i}) | \leq t_{i}$ . The hypergraph ℋ is colorable if it admits at least one proper coloring. We consider hypergraphs ℋ over a “host graph”, that means a graph G on the same vertex set X as ℋ, such that each $E_{i}$ induces a connected subgraph in G. In the current...

Colouring planar mixed hypergraphs.

Kündgen, André; Mendelsohn, Eric; Voloshin, Vitaly — 2000

The Electronic Journal of Combinatorics [electronic only]

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About uniquely colorable mixed hypertrees

Color-bounded hypergraphs, V: host graphs and subdivisions

Colouring planar mixed hypergraphs.