On the existence of (k, l)-critical graphs

Research output: Contribution to journalArticle

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Abstract

CWI, Kruislaan 413, 1098 SJ, Amsterdam, The Netherlands Let W ⊆ V in a graph G = (V, E) such that W ∩ X ≠ ∅ for each fragment X of G. Then G is defined to be W-locally (k, l)-critical if κ(G - W′) = k - |W′| holds for every W′ ⊆ W with |W′| ≤ l. In this note we give a short proof for the following recent result of Su: every non-complete W-locally (k, l)-critical graph has (2l + 2) distinct ends and |W| ≥ 2l + 2. (This result implies that Slater's conjecture is true: there exist no (k, l)-critical graphs with 2l > k, except Kk + 1.).

Original languageEnglish
Pages (from-to)273-275
Number of pages3
JournalDiscrete Mathematics
Volume179
Issue number1-3
Publication statusPublished - Jan 15 1998

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Critical Graph
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ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Theoretical Computer Science

Cite this

On the existence of (k, l)-critical graphs. / Jordán, T.

In: Discrete Mathematics, Vol. 179, No. 1-3, 15.01.1998, p. 273-275.

Research output: Contribution to journalArticle

Jordán, T. / On the existence of (k, l)-critical graphs. In: Discrete Mathematics. 1998 ; Vol. 179, No. 1-3. pp. 273-275.
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