Chromatic-Index-Critical Graphs of Orders 11 and 12

@article{Brinkmann1998ChromaticIndexCriticalGO,
  title={Chromatic-Index-Critical Graphs of Orders 11 and 12},
  author={Gunnar Brinkmann and Eckhard Steffen},
  journal={Eur. J. Comb.},
  year={1998},
  volume={19},
  pages={889-900}
}
Abstract A chromatic-index-critical graphGonnvertices is non-trivial if it has at most Δ ⌊ n 2 ⌋ edges. We prove that there is no chromatic-index-critical graph of order 12, and that there are precisely two non-trivial chromatic-index-critical graphs on 11 vertices. Together with known results this implies that there are precisely three non-trivial chromatic-index-critical graphs of order ≤12. 
View via Publisher
26 Citations
Highly Influential Citations
2
Background Citations
11
Methods Citations
1
Results Citations
1

26 Citations

Edge Chromatic 5 - Critical Graphs of Order 15
New results on chromatic index critical graphs
Independent sets and 2‐factors in edge‐chromatic‐critical graphs
TLDR
Both conjectures for critical graphs which are critical with respect to the chromatic index are proved, and upper bounds for the size of independent vertex sets in those graphs are determined.
Chromatic-index-critical graphs of orders 13 and 14
Lower bounds on the number of edges in edge-chromatic-critical graphs with fixed maximum degrees
Edge coloring of graphs with small maximum degrees
Factors of edge-chromatic critical graphs: a brief survey and some equivalences
This article discusses the main results that have been derived till date on some conjectures on factors of critical graphs. It provides some equivalent formulations of Vizing’s 2-factor conjecture,…
Special Classes of Snarks
We report the most relevant results on the classification, up to isomorphism, of nontrivial simple uncolorable (i.e., the chromatic index equals 4) cubic graphs, called snarks in the literature. Then…
Excessive Factorizations of Regular Graphs
TLDR
It is shown that the size of an excessive factorization of a regular graph can exceed the degree of the graph by an arbitrarily large quantity.
Generation of various classes of trivalent graphs
...
...

References

SHOWING 1-10 OF 29 REFERENCES
On small graphs critical with respect to edge colourings
On critical graphs with chromatic index 4
The chromatic index of graphs with a spanning star
TLDR
A proof of that conjecture and a corollary that helps determine the chromatic index of some graphs with 2s points and maximum degree 2s − 2 are presented.
The chromatic index of graphs of even order with many edges
We show that, for r = 1, 2, a graph G with 2n + 2 (6) vertices and maximum degree 2n + 1 - r is of Class 2 if and only if |E(G/v)| > () - rn, where v is a vertex of G of minimum degree, and we make a…
3- and 4-critical Graphs of Small Even Order
Regular Graphs of High Degree are 1‐Factorizable
It is a well-known conjecture that if a regular graph G of order 2n has degree d(G) satisfying d(G) n, then G is the union of edge-disjoint 1-factors. It is well known that this conjecture is true…
Edge‐Colorings of Graphs: A Progress Report
It is almost ten years since the appearance of S. Fiorini and R. J. Wilson’s monograph Edge-Colourings of Graphs [21]. In this expository paper we outline some of the progress on edge-colorings since…
Some Topics in Graph Theory
1. Basic terminology 2. Edge-colourings of graphs 3. Symmetries in graphs 4. Packing of graphs 5. Computational complexity of graph properties.
sa, Problem ceteriju boja (The Problem of four Colors), Hrvatsko Prirodoslovno Dru stvo Glasnik Math.-Fiz
  • Astr. Ser. II
  • 1946
On an estimate of the chromatic class of a p-graph
  • Diskret. Anal. 3
  • 1964
...
...