Atoms of cyclic connectivity in cubic graphs
Roman Nedela, Martin Škoviera (1995)
Mathematica Slovaca
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Displaying similar documents to “Nonexistence of graphs with cyclic defect.”
Atoms of cyclic connectivity in cubic graphs
Alternating cycles and realizations of a degree sequence
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Heavy Subgraph Conditions for Longest Cycles to Be Heavy in Graphs
Binlong Lia, Shenggui Zhang (2016)
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Let G be a graph on n vertices. A vertex of G with degree at least n/2 is called a heavy vertex, and a cycle of G which contains all the heavy vertices of G is called a heavy cycle. In this note, we characterize graphs which contain no heavy cycles. For a given graph H, we say that G is H-heavy if every induced subgraph of G isomorphic to H contains two nonadjacent vertices with degree sum at least n. We find all the connected graphs S such that a 2-connected graph G being S-heavy implies...
Characterization of -minimally nonouterplanar join graphs
D. G. Akka, J. K. Bano (2001)
Mathematica Bohemica
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In this paper, we present characterizations of pairs of graphs whose join graphs are 2-minimally nonouterplanar. In addition, we present a characterization of pairs of graphs whose join graphs are 2-minimally nonouterplanar in terms of forbidden subgraphs.
Large Degree Vertices in Longest Cycles of Graphs, I
Binlong Li, Liming Xiong, Jun Yin (2016)
Discussiones Mathematicae Graph Theory
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In this paper, we consider the least integer d such that every longest cycle of a k-connected graph of order n (and of independent number α) contains all vertices of degree at least d.