Let \(G\) be a graph with minimum degree \(\delta(G)\). R.P. Gupta proved two interesting results: 1) A bipartite graph \(G\) has a 5-edge-coloring in which all 6 colors appear at each vertex. 2) If \(G\) is a simple graph with \(\delta(G) > 1\), then \(G\) has a \((\delta – 1)\)-edge-coloring in which all \((\delta – 1)\) colors appear at each vertex. Let \(t\) be a positive integer. In this paper, we extend the first result by showing that for every bipartite graph, there exists a \(t\)-edge coloring such that at each vertex \(v\), \(\min\{t, d(v)\}\) colors appear. Additionally, we demonstrate that if \(G\) is a graph, then the edges of \(G\) can be colored using \(t\) colors, where for each vertex \(v\), the number of colors appearing at \(v\) is at least \(\min\{t, d(v) – 1\}\), generalizing the second result.