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On vertex-degree restricted paths in $4$-connected planar graphs

In: Tatra Mountains Mathematical Publications, vol. 18, no. 4
Erhard Hexel - Hansjoachim Walther
Detaily:
Rok, strany: 1999, 1 - 13
O článku:
Every $4$-connected planar graph $G$ is proved either to contain no $k$-path or to have a $k$-path containing no vertex of degree $≥ 2k+4$ if $δ(G)≥ 4$ or of degree $≥ k+5$ if $δ(G)=5$, respectively. There are $4$-connected planar graphs such that each $k$-path contains a vertex of degree $≥ 2k+2$ if $δ(G)≥ 4$ or $≥ k+1$ if $δ (G)=5$ and $k≥ 15$. There are $5$-connected planar graphs such that each $k$-path contains a vertex of degree $≥lfloor (2k+8)/3 floor$ if $k≥ 20$.
Ako citovať:
ISO 690:
Hexel, E., Walther, H. 1999. On vertex-degree restricted paths in $4$-connected planar graphs. In Tatra Mountains Mathematical Publications, vol. 18, no.4, pp. 1-13. 1210-3195.

APA:
Hexel, E., Walther, H. (1999). On vertex-degree restricted paths in $4$-connected planar graphs. Tatra Mountains Mathematical Publications, 18(4), 1-13. 1210-3195.