On the Size of Edge Chromatic Critical Graphs

Abstract

In this paper, by applying the discharging method, we prove that if G ¼ ðV ; EÞ is a D-critical graph, then jEj5

New lower bounds for the size of edge chromatic critical graphs

“…But for Á 2 f6; 7; 8; 9; 11g, the lower bounds in [1,4] are still better. In this paper, by applying the discharging method again, we obtain new lower bounds for the size of edge chromatic critical graphs and improve results in [1,4,8] for Á 2 f6; . .…”

“…2. From the proof of our theorem, it is conceivable that for each fixed Á, one can use the discharging method to improve the result in [8]. However, one can easily see that the larger Á is, the more discharging rules are needed.…”

“…However, one can easily see that the larger Á is, the more discharging rules are needed. Hence it is still not clear how to improve the result of [8] in general. One thing is clear that to get better bounds for the size of edge chromatic critical graphs, one needs more structural results about edge chromatic critical graphs.…”

“…f ðÁÞn, where f ðÁÞ ¼ The method in [1,4] is similar to the one in [2] and furthermore, the difference between the coefficients of n in [1,4] and [2] is bounded by 5 4 and thus it is independent of Á. Recently, by introducing the discharging method into the problem of searching better lower bounds for the size of edge chromatic critical graphs, it was proved in [8]…”

The average degree of an edge‐chromatic critical graph II

“…We will prove Theorem 1.1 (a) first, and then show how the argument can be refined so as to prove Theorem 1.1 (b) and (c). The structure of the proof is based on the proof by Sanders and Zhao of ( [6], Theorem 2). 1.1 (a).…”