Abstract
AbstractA finite simple connected graph G with maximum degree k is k-critical if it has chromatic index $$\chi '(G)=k+1$$
χ
′
(
G
)
=
k
+
1
and $$\chi '(G-e)=k$$
χ
′
(
G
-
e
)
=
k
for every edge $$e\in E(G)$$
e
∈
E
(
G
)
. Bej and the first author [2] raised the question whether every k-critical graph has an even factor. We prove that every k-critical graphs with at most $$2k-6$$
2
k
-
6
vertices of degree 2 has an even factor.
Funder
deutsche forschungsgemeinschaft
Universität Paderborn
Publisher
Springer Science and Business Media LLC
Subject
Discrete Mathematics and Combinatorics,Theoretical Computer Science
Reference10 articles.
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2. Bej, S., Steffen, E.: Factors of edge-chromatic critical graphs: a brief survey and some equivalences, Selected topics in graph theory and its applications, 37 - 48, Lect. Notes Semin. Interdiscip. Mat. 14, Semin. Interdiscip. Mat. (S.I.M.), Potenza (2017)
3. Chen, G., Shan, S.: Vizing’s 2-factor conjecture involving large maximum degree. J. Graph Theory 86, 422–438 (2017)
4. Chen, X., Ji, Q., Liu, M.: Reducing Vizing’s 2-factor conjecture to Meredith extension of critical graphs. Graphs Comb. 36, 1585–1591 (2020)
5. Fleischner, H.: Spanning eulerian subgraphs, the Splitting Lemma, and Petersen’s Theorem. Disc. Math. 101, 33–37 (1992)
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