Embedding a forest in a graph.
Goldberg, Mark K., Magdon-Ismail, Malik (2011)
The Electronic Journal of Combinatorics [electronic only]
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Goldberg, Mark K., Magdon-Ismail, Malik (2011)
The Electronic Journal of Combinatorics [electronic only]
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Van Bussel, Frank (2002)
The Electronic Journal of Combinatorics [electronic only]
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Faudree, Jill, Faudree, Ralph J., Gould, Ronald J., Jacobson, Michael S. (2009)
The Electronic Journal of Combinatorics [electronic only]
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DeLaViña, Ermelinda, Waller, Bill (2008)
The Electronic Journal of Combinatorics [electronic only]
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Bohdan Zelinka (1994)
Mathematica Bohemica
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An extended tree of a graph is a certain analogue of spanning tree. It is defined by means of vertex splitting. The properties of these trees are studied, mainly for complete graphs.
Bohdan Zelinka (1979)
Časopis pro pěstování matematiky
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Jackson, Bill, Sokal, Alan D. (2010)
The Electronic Journal of Combinatorics [electronic only]
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Ralph J. Faudree, Ronald J. Gould, Michael S. Jacobson (2013)
Discussiones Mathematicae Graph Theory
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For a fixed graph F, a graph G is F-saturated if there is no copy of F in G, but for any edge e ∉ G, there is a copy of F in G + e. The minimum number of edges in an F-saturated graph of order n will be denoted by sat(n, F). A graph G is weakly F-saturated if there is an ordering of the missing edges of G so that if they are added one at a time, each edge added creates a new copy of F. The minimum size of a weakly F-saturated graph G of order n will be denoted by wsat(n, F). The graphs...
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...