Degree Sets for Triangle‐free Graphs

Kapoor, Sanjiv; Lesniak-Foster, Linda M.

doi:10.1111/j.1749-6632.1979.tb32806.x

Cited by 8 publications

(6 citation statements)

References 2 publications

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“…the degree sequence without multiplicities. Kapoor, Polimeni, and Wall [8] characterized all possible degree sets for n-vertex graphs in general as well as n-vertex trees, outerplanar graphs and planar graphs.…”

Section: Resultsmentioning

confidence: 99%

Extremal problems for chromatic neighborhood sets

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Molloy

2002

Journal of Graph Theory

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Abstract:The chromatic neighborhood sequence of a graph G is the list of the chromatic numbers of the subgraphs induced by the neighborhoods of the vertices. We study the maximum multiplicity of this sequence, proving, amongst other things, that if a chromatic neighborhood sequence has t distinct values, the largest value being d t , then there is a value with multiplicity at least 2d t t (1ÀÂ (ln t/t)). This bound is asymptotically tight.

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Section: Resultsmentioning

confidence: 99%

Extremal problems for chromatic neighborhood sets

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Molloy

2002

Journal of Graph Theory

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“…Of course, the degree set of an Eulerian graph consists only of even integers. Kapoor, Polimeni, and Wall [30] showed that if S = { k , , k 2 , . .…”

Section: Fleury's Algorithmmentioning

confidence: 99%

An Eulerian exposition

Lesniak

Oellermann

1986

Journal of Graph Theory

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An overview of Eulerian graphs is presented. In particular, characterizations of Eulerian graphs and digraphs as well as algorithms for constructing Eulerian circuits are discussed. A solution to the Chinese postman problem is followed by a study of subgraphs and supergraphs of Eulerian graphs. After an introduction to randomly Eulerian graphs and digraphs, w e conclude with a summary of a variety of results involving enumeration.We discuss some of the many topics related to Eulerian multigraphs and multidigraphs. In Section 1, results related to characterizations of Eulerian multigraphs and multidigraphs as well as some algorithms are studied. Section 2 concentrates on the Chinese postman problem, which is one example of embedding a graph in an Eulerian multigraph, whereas Section 3 discusses the question of embedding a graph in an Eulerian graph. Further, Section 3 includes results on Eulerian subgraphs of a graph. Section 4 is concerned with randomly Eulerian multigraphs and multidigraphs. We close with a discussion of some enumeration results relating to Eulerian multigraphs and multidigraphs.

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“…The degree set D G = {a,, a,, .... ak} of a graph G is the set of degrees (valencies) of the vertices of G. Clearly, we can assume that a , < u2 < * * * < u k (see [41]). …”

Section: Graphs With Prescribed Degree Sets a N D Girthmentioning

confidence: 99%