Bibliographic Details
| Title: |
On induced subgraphs of H(n, 3) with maximum degree 1. |
| Authors: |
Potechin, Aaron1, Tsang, Hing Yin1 |
| Source: |
Discrete Mathematics & Theoretical Computer Science (DMTCS). 2026, Vol. 28 Issue 2, p1-41. 41p. |
| Subjects: |
Independent sets, Subgraphs, Discrete mathematics, Combinatorics, Graph theory |
| Abstract: |
In this paper, we consider induced subgraphs of the Hamming graph H(n, 3). We show that if U ⊆ Z n 3 and U induces a subgraph of H(n, 3) with maximum degree at most 1 then 1. If U is disjoint from a maximum size independent set of H(n, 3) then |U| ≤ 3 n−1 + 1. Moreover, all such U with size 3 n−1 + 1 are isomorphic to each other. 2. For n ≥ 6, there exists such a U with size |U| = 3n−1 + 18 and this is optimal for n = 6. 3. If U ∩ {x, x + e1, x + 2e1} ̸= ϕ for all x ∈ Z n 3 then |U| ≤ 3 n−1 + 81. [ABSTRACT FROM AUTHOR] |
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| Database: |
Engineering Source |
