Strong products of ?-critial graphs.
Sandi Klavzar (1993)
Aequationes mathematicae
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Sandi Klavzar (1993)
Aequationes mathematicae
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P.A. Winter, Henda C. Swart (1986)
Aequationes mathematicae
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Frank Harary, Roberto Frucht (1970)
Aequationes mathematicae
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Lucas C. van der Merwe, Cristine M. Mynhardt, Teresa W. Haynes (2001)
Discussiones Mathematicae Graph Theory
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Denote the total domination number of a graph G by γₜ(G). A graph G is said to be total domination edge critical, or simply γₜ-critical, if γₜ(G+e) < γₜ(G) for each edge e ∈ E(G̅). For 3ₜ-critical graphs G, that is, γₜ-critical graphs with γₜ(G) = 3, the diameter of G is either 2 or 3. We characterise the 3ₜ-critical graphs G with diam G = 3.
Ian Anderson (1982)
Aequationes mathematicae
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A.K. Dewdney (1970)
Aequationes mathematicae
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K.B. Chilakamarri, Carolyn R. Mahoney (1995)
Aequationes mathematicae
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Andrey A. Dobrynin, Leonid S. Mel&#039;nikov, Artem V. Pyatkin (2007)
Discussiones Mathematicae Graph Theory
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In 1960, Dirac put forward the conjecture that r-connected 4-critical graphs exist for every r ≥ 3. In 1989, Erdös conjectured that for every r ≥ 3 there exist r-regular 4-critical graphs. A method for finding r-regular 4-critical graphs and the numbers of such graphs for r ≤ 10 have been reported in [6,7]. Results of a computer search for graphs of degree r = 12,14,16 are presented. All the graphs found are both r-regular and r-connected.
M. Borowiecki (1972)
Colloquium Mathematicae
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Odile Favaron (1996)
Discussiones Mathematicae Graph Theory
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A graph is said to be k-factor-critical if the removal of any set of k vertices results in a graph with a perfect matching. We study some properties of k-factor-critical graphs and show that many results on q-extendable graphs can be improved using this concept.
L.D. Andersen, C. Thomassen (1980)
Aequationes mathematicae
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Pavol Hell, A. Kotzig, A. Rosa (1975)
Aequationes mathematicae
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