Remarks on the size of critical edge-chromatic graphs

AbstractWe give new lower bounds for the size of Δ-critical edge-chromatic graphs when 6 ⩽ Δ ⩽ 21

The average degree of a multigraph critical with respect to edge or total choosability

AbstractLet G be a multigraph with maximum degree at most Δ⩾3 such that ch′(G)>Δ or ch″(G)>Δ+1 and G is minimal with this property. A new proof is given for the result (which was already known, apart from a simple calculation) that the average degree of G is greater than 2Δ except possibly in the second case when Δ=5

Edge coloring of simple graphs and edge -face coloring of simple plane graphs

We prove that chie( G) = Delta if Delta ≥ 5 and g ≥ 4, or Delta ≥ 4 and g ≥ 5, or Delta ≥ 3 and g ≥ 9. In addition, if chi(Sigma) \u3e 0, then chie( G) = Delta if Delta ≥ 3 and g ≥ 8 where Delta, g is the maximum degree, the girth of the graph G, respectively.;It is proved that G is not critical if d¯ ≤ 6 and Delta ≥ 8, or d¯ ≤ 203 and Delta ≥ 9. This result generalizes earlier results.;Given a simple plane graph G, an edge-face k-coloring of G is a function &phis; : E(G) ∪ F(G) {lcub}1, ···, k{rcub} such that, for any two adjacent elements a, b ∈ E(G) ∪ F(G), &phis;( a) ≠ &phis;(b). Denote chie( G), chief(G), Delta( G) the edge chromatic number, the edge-face chromatic number and the maximum degree of G, respectively. We prove that chi ef(G) = chie( G) = Delta(G) for any 2-connected simple plane graph G with Delta(G) ≥ 24

On The Size Of Edge Chromatic Critical Graphs

In this paper, by applying the discharging method, we prove that if G = (V, E) is a Δ-critical graph, then E ≥1/4 V (Δ + √2Δ - 1). © 2002 Elsevier, Science (USA)

On the size of edge chromatic critical graphs

In this paper, by applying the discharging method, we prove that if G = (V, E) is a Delta-critical graph, then \E\ greater than or equal to 1/4\V\(Delta + root2Delta-1). (C) 2002 Elsevier Science (USA)

On The Size Of Edge Chromatic Critical Graphs

In this paper, by applying the discharging method, we prove that if G = (V, E) is a Δ-critical graph, then E ≥1/4 V (Δ + √2Δ - 1). © 2002 Elsevier, Science (USA)