Degree sequences of graphs containing a cycle with prescribed length
Czechoslovak Mathematical Journal (2009)
- Volume: 59, Issue: 2, page 481-487
- ISSN: 0011-4642
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topYin, Jian Hua. "Degree sequences of graphs containing a cycle with prescribed length." Czechoslovak Mathematical Journal 59.2 (2009): 481-487. <http://eudml.org/doc/37935>.
@article{Yin2009,
abstract = {Let $r\ge 3$, $n\ge r$ and $\pi =(d_1,d_2,\ldots ,d_n)$ be a non-increasing sequence of nonnegative integers. If $\pi $ has a realization $G$ with vertex set $V(G)=\lbrace v_1,v_2,\ldots ,v_n\rbrace $ such that $d_G(v_i)=d_i$ for $i=1,2,\ldots , n$ and $v_1v_2\cdots v_rv_1$ is a cycle of length $r$ in $G$, then $\pi $ is said to be potentially $C_r^\{\prime \prime \}$-graphic. In this paper, we give a characterization for $\pi $ to be potentially $C_r^\{\prime \prime \}$-graphic.},
author = {Yin, Jian Hua},
journal = {Czechoslovak Mathematical Journal},
keywords = {graph; degree sequence; potentially $C_r$-graphic sequence; graph; degree sequence; potentially -graphic sequence},
language = {eng},
number = {2},
pages = {481-487},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Degree sequences of graphs containing a cycle with prescribed length},
url = {http://eudml.org/doc/37935},
volume = {59},
year = {2009},
}
TY - JOUR
AU - Yin, Jian Hua
TI - Degree sequences of graphs containing a cycle with prescribed length
JO - Czechoslovak Mathematical Journal
PY - 2009
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 59
IS - 2
SP - 481
EP - 487
AB - Let $r\ge 3$, $n\ge r$ and $\pi =(d_1,d_2,\ldots ,d_n)$ be a non-increasing sequence of nonnegative integers. If $\pi $ has a realization $G$ with vertex set $V(G)=\lbrace v_1,v_2,\ldots ,v_n\rbrace $ such that $d_G(v_i)=d_i$ for $i=1,2,\ldots , n$ and $v_1v_2\cdots v_rv_1$ is a cycle of length $r$ in $G$, then $\pi $ is said to be potentially $C_r^{\prime \prime }$-graphic. In this paper, we give a characterization for $\pi $ to be potentially $C_r^{\prime \prime }$-graphic.
LA - eng
KW - graph; degree sequence; potentially $C_r$-graphic sequence; graph; degree sequence; potentially -graphic sequence
UR - http://eudml.org/doc/37935
ER -
References
top- Berge, C., Graphs and Hypergraphs, North Holland Amsterdam (1973). (1973) Zbl0254.05101MR0357172
- Erdős, P., Gallai, T., Graphs with given degrees of vertices, Math. Lapok 11 (1960), 264-274. (1960)
- Fulkerson, D. R., Hoffman, A. J., Mcandrew, M. H., 10.4153/CJM-1965-016-2, Canad. J. Math. 17 (1965), 166-177. (1965) Zbl0132.21002MR0177908DOI10.4153/CJM-1965-016-2
- Gould, R. J., Jacobson, M. S., Lehel, J., Potentially -graphical degree sequences, In: Combinatorics, Graph Theory, and Algorithms, Vol. 1 Y. Alavi et al. New Issues Press Kalamazoo Michigan (1999), 451-460. (1999) MR1985076
- Kézdy, A. E., Lehel, J., Degree sequences of graphs with prescribed clique size, In: Combinatorics, Graph Theory, and Algorithms, Vol. 2 Y. Alavi New Issues Press Kalamazoo Michigan (1999), 535-544. (1999) MR1985084
- Lai, C., The smallest degree sum that yields potentially -graphical sequences, J. Combin. Math. Combin. Comput. 49 (2004), 57-64. (2004) Zbl1054.05027MR2054962
- Rao, A. R., The clique number of a graph with given degree sequence, Graph Theory, Proc. Symp. Calcutta 1976, ISI Lecture Notes 4 A. R. Rao (1979), 251-267. (1979)
- Rao, A. R., An Erdős-Gallai type result on the clique number of a realization of a degree sequence, Unpublished.
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