An Approximation Algorithm for Diagnostic Test Scheduling in Multicomputer Systems
IEEE Transactions on Computers
Scheduling file transfers for trees and odd cycles
SIAM Journal on Computing
Graph Theory With Applications
Graph Theory With Applications
Some results about f-critical graphs
Networks
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An f-coloring of a graph G is an edge-coloring of G such that each color appears at each vertex v 驴 V(G) at most f(v) times. The minimum number of colors needed to f-color G is called the f-chromatic index of G, and denoted by 驴驴 f (G). Any simple graph G has f-chromatic index equal to Δ f (G) or Δ f (G) + 1, where $\Delta_{f}(G)=\max_{v\in V(G)}\{\lceil\frac{d(v)}{f(v)}\rceil\}$. If 驴驴 f (G) = Δ f (G), then G is of f-class 1; otherwise G is of f-class 2. In this paper, we show that if f(v) is positive and even for all $v\in V_0^*(G)\cup N_G(V_0^*(G))$, then G is of f-class 1, where $V^{*}_{0}(G)=\{v\in V(G):\frac{d(v)}{f(v)}=\Delta_{f}(G)\}$ and $N_G(V_0^*(G))=\{v\in V(G):uv\in E(G), u\in V_0^*(G)\}$. This result improves the simple graph version of a result of Hakimi and Kariv [4].