Irregular embeddings of multigraphs with fixed chromatic number
نویسندگان
چکیده
Let G be a c-chromatic multigraph (c >t 2) with maximum edge multiplicity s. In this note we show that G has an embedding as an induced subgraph, into some degree irregular c-chromatic multigraph having the same maximum edge multiplicity.
منابع مشابه
Asymptotics of the total chromatic number for multigraphs
For loopless multigraphs, the total chromatic number is asymptotically its fractional counterpart as the latter invariant tends to infinity. The proof of this is based on a recent theorem of Kahn establishing the analogous asymptotic behaviour of the list-chromatic index for multigraphs. The total colouring conjecture, proposed independently by Behzad [1] and Vizing [11], asserts that the total...
متن کاملChromatic Edge Strength of Some Multigraphs
The edge strength s(G) of a multigraph G is the minimum number of colors in a minimum sum edge coloring of G. We give closed formulas for the edge strength of bipartite multigraphs and multicycles. These are shown to be classes of multigraphs for which the edge strength is always equal to the chromatic index.
متن کاملChromatic polynomials of some nanostars
Let G be a simple graph and (G,) denotes the number of proper vertex colourings of G with at most colours, which is for a fixed graph G , a polynomial in , which is called the chromatic polynomial of G . Using the chromatic polynomial of some specific graphs, we obtain the chromatic polynomials of some nanostars.
متن کاملSome maximum multigraphs and adge/vertex distance colourings
Shannon–Vizing–type problems concerning the upper bound for a distance chromatic index of multigraphs G in terms of the maximum degree ∆(G) are studied. Conjectures generalizing those related to the strong chromatic index are presented. The chromatic d–index and chromatic d–number of paths, cycles, trees and some hypercubes are determined. Among hypercubes, however, the exact order of their gro...
متن کاملGroup colorability of multigraphs
Let G be a multigraph with a fixed orientation D and let Γ be a group. Let F(G, Γ ) denote the set of all functions f : E(G) → Γ . A multigraph G is Γ -colorable if and only if for every f ∈ F(G, Γ ), there exists a Γ -coloring c : V (G) → Γ such that for every e = uv ∈ E(G) (assumed to be directed from u to v), c(u)c(v)−1 ≠ f (e). We define the group chromatic number χg (G) to be the minimum i...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- Discrete Mathematics
دوره 145 شماره
صفحات -
تاریخ انتشار 1995