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  "path": "/abs/2605.24258v1",
  "publishedAt": "2026-05-26T00:00:00.000Z",
  "site": "https://arxiv.org",
  "tags": [
    "Stefan Bard",
    "Gary MacGillivray",
    "Jacobus Swarts"
  ],
  "textContent": "**Authors:** Stefan Bard, Gary MacGillivray, Jacobus Swarts\n\nFor an integer $t \\geq 1$, a homomorphism of a digraph G to a digraph $H$ is $t$-frugal if no more than $t$ in-neighbours of any vertex of $G$ have the same image. There is a dichotomy theorem based on structural properties when $t=1$ and $H$ has a loop at each vertex, but there is unlikely to be such a theorem for general digraphs $H$. For $t \\geq 2$ we describe a structural dichotomy theorem for $t$-frugal homomorphisms of general digraphs.",
  "title": "The complexity of frugal digraph homomorphisms"
}