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2012 | 32 | 4 | 607-615
Tytuł artykułu

The i-chords of cycles and paths

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
An i-chord of a cycle or path is an edge whose endpoints are a distance i ≥ 2 apart along the cycle or path. Motivated by many standard graph classes being describable by the existence of chords, we investigate what happens when i-chords are required for specific values of i. Results include the following: A graph is strongly chordal if and only if, for i ∈ {4,6}, every cycle C with |V(C)| ≥ i has an (i/2)-chord. A graph is a threshold graph if and only if, for i ∈ {4,5}, every path P with |V(P)| ≥ i has an (i -2)-chord.
Wydawca
Rocznik
Tom
32
Numer
4
Strony
607-615
Opis fizyczny
Daty
wydano
2012
otrzymano
2011-07-29
poprawiono
2011-11-04
zaakceptowano
2011-11-04
Twórcy
  • Department of Mathematics and Statistics, Wright State University, Dayton, Ohio 45435 USA
Bibliografia
  • [1] H.-J. Bandelt and H.M. Mulder, Distance-hereditary graphs, J. Combin. Theory (B) 41 (1986) 182-208, doi: 10.1016/0095-8956(86)90043-2.
  • [2] A. Brandstädt, V.B. Le and J.P. Spinrad, Graph Classes: A Survey (Society for Industrial and Applied Mathematics, Philadelphia, 1999).
  • [3] M.B. Cozzens and L.L. Kelleher, Dominating cliques in graphs, Discrete Math. 86 (1990) 101-116, doi: 10.1016/0012-365X(90)90353-J.
  • [4] M. Farber, Characterizations of strongly chordal graphs, Discrete Math. 43 (1983) 173-189, doi: 10.1016/0012-365X(83)90154-1.
  • [5] E. Howorka, A characterization of ptolemaic graphs, J. Graph Theory 5 (1981) 323-331, doi: 10.1002/jgt.3190050314.
  • [6] J. Liu and H.S. Zhou, Dominating subgraphs in graphs with some forbidden structures, Discrete Math. 135 (1994) 163-168, doi: 10.1016/0012-365X(93)E0111-G.
  • [7] N.V.R. Mahadev and U.N. Peled, Threshold Graphs and Related Topics (North-Holland, Amsterdam, 1995).
  • [8] A. McKee, Constrained chords in strongly chordal and distance-hereditary graphs, Utilitas Math. 87 (2012) 3-12.
  • [9] T.A. McKee and F.R. McMorris, Topics in Intersection Graph Theory (Society for Industrial and Applied Mathematics, Philadelphia, 1999).
  • [10] E.S. Wolk, The comparability graph of a tree, Proc. Amer. Math. Soc. 13 (1962) 789-795, doi: 10.1090/S0002-9939-1962-0172273-0.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1629
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