Abstract
In 1970, Dirac conjectured that for each integer k ≥ 4, there exists a vertex k-critical graph without any critical edge. In this paper, we introduce strict-vertex critically (k − 1)-de-chromatic pair, strict 2-vertex decomposition graph and so on. By studying their relevant properties, we obtain that any vertex k-critical graph without any critical edge generates an infinite family of vertex k-critical graphs without critical edges.
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Wang, J. (2009). Infinite Family from Each Vertex k-Critical Graph without Any Critical Edge. In: Du, DZ., Hu, X., Pardalos, P.M. (eds) Combinatorial Optimization and Applications. COCOA 2009. Lecture Notes in Computer Science, vol 5573. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-02026-1_22
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DOI: https://doi.org/10.1007/978-3-642-02026-1_22
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-02025-4
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