Bounds for the chromatic index of signed multigraphs
نویسندگان
چکیده
The paper studies edge-coloring of signed multigraphs and extends classical Theorems Shannon K\"onig to multigraphs. We prove that the chromatic index a multigraph $(G,\sigma_G)$ is at most $\lfloor \frac{3}{2} \Delta(G) \rfloor$. Furthermore, balanced $(H,\sigma_H)$ $\Delta(H) + 1$ with $\Delta(H)$ are characterized.
منابع مشابه
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It is well known that if G is a multigraph then χ(G) ≥ χ(G) := max{∆(G), Γ(G)}, where χ(G) is the chromatic index of G, χ(G) is the fractional chromatic index of G, ∆(G) is the maximum degree of G, and Γ(G) = max{2|E(G[U ])|/(|U | − 1) : U ⊆ V (G), |U | ≥ 3, |U | is odd}. The conjecture that χ(G) ≤ max{∆(G) + 1, dΓ(G)e} was made independently by Goldberg (1973), Anderson (1977), and Seymour (19...
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ژورنال
عنوان ژورنال: Discrete Applied Mathematics
سال: 2023
ISSN: ['1872-6771', '0166-218X']
DOI: https://doi.org/10.1016/j.dam.2023.05.008