On small graphs critical with respect to edge colourings

DOI10.1016/0012-365X(76)90139-4zbMath0344.05121MaRDI QIDQ1232418

Lowell W. Beineke, Stanley Fiorini

Publication date: 1976

Published in: Discrete Mathematics (Search for Journal in Brave)

Mathematics Subject Classification ID

Relations of low-dimensional topology with graph theory (57M15) Coloring of graphs and hypergraphs (05C15)

Related Items (24)

On the size of edge-chromatic critical graphs ⋮ Finding Δ(Σ) for a surface σ of characteristic χ(Σ) = −5 ⋮ There are no edge-chromatic 4-critical graphs of order 12 ⋮ Hamiltonian cycles in critical graphs with large maximum degree ⋮ A Sufficient Condition for Edge Chromatic Critical Graphs to Be Hamiltonian—An Approach to Vizing's 2‐Factor Conjecture ⋮ On the size of graphs of class 2 whose cores have maximum degree two ⋮ Linear algorithms for edge-coloring trees and unicyclic graphs ⋮ Finding \(\Delta (\Sigma)\) for a surface \(\Sigma \) of characteristic \(-6\) and \(-7\) ⋮ Sizes of critical graphs with small maximum degrees ⋮ Lower bounds on the number of edges in edge-chromatic-critical graphs with fixed maximum degrees ⋮ On the average degree of critical graphs with maximum degree six ⋮ Some criteria for a graph to be class 1 ⋮ Edge coloring of graphs with small average degrees ⋮ On graphs critical with respect to edge-colourings ⋮ Finding the exact bound of the maximum degrees of class two graphs embeddable in a surface of characteristic \(\epsilon \in \{-1, -2, -3\}\) ⋮ A note on class one graphs with maximum degree six ⋮ The size of edge chromatic critical graphs with maximum degree 6 ⋮ Remarks on the critical graph conjecture ⋮ Clique-perfectness of complements of line graphs ⋮ Finding Δ(Σ) for a Surface Σ of Characteristic −4 ⋮ New results on chromatic index critical graphs ⋮ Edge coloring of graphs with small maximum degrees ⋮ Chromatic index critical graphs of order 9 ⋮ A brief history of edge-colorings – with personal reminiscences

Cites Work

• On critical graphs with chromatic index 4
• Some remarks on the chromatic index of a graph
• On the edge-chromatic number of a graph
• On the Girth of Graphs Critical with Respect to Edge-Colourings
• The Factorization of Linear Graphs
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