On graphs with prescribed edge neighbourhoods
Dalibor Fronček (1989)
Commentationes Mathematicae Universitatis Carolinae
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Dalibor Fronček (1989)
Commentationes Mathematicae Universitatis Carolinae
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Černý, A., Horák, P., Rosa, A., Znám, Š. (1996)
Acta Mathematica Universitatis Comenianae. New Series
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Pavel Hrnčiar (1990)
Czechoslovak Mathematical Journal
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Daniel W. Cranston, Sogol Jahanbekam, Douglas B. West (2014)
Discussiones Mathematicae Graph Theory
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The 1, 2, 3-Conjecture states that the edges of a graph without isolated edges can be labeled from {1, 2, 3} so that the sums of labels at adjacent vertices are distinct. The 1, 2-Conjecture states that if vertices also receive labels and the vertex label is added to the sum of its incident edge labels, then adjacent vertices can be distinguished using only {1, 2}. We show that various configurations cannot occur in minimal counterexamples to these conjectures. Discharging then confirms...
Zsolt Tuza (1989)
Acta Universitatis Carolinae. Mathematica et Physica
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