# Paths with restricted degrees of their vertices in planar graphs

Czechoslovak Mathematical Journal (1999)

- Volume: 49, Issue: 3, page 481-490
- ISSN: 0011-4642

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topJendroľ, Stanislav. "Paths with restricted degrees of their vertices in planar graphs." Czechoslovak Mathematical Journal 49.3 (1999): 481-490. <http://eudml.org/doc/30500>.

@article{Jendroľ1999,

abstract = {In this paper it is proved that every $3$-connected planar graph contains a path on $3$ vertices each of which is of degree at most $15$ and a path on $4$ vertices each of which has degree at most $23$. Analogous results are stated for $3$-connected planar graphs of minimum degree $4$ and $5$. Moreover, for every pair of integers $n\ge 3$, $ k\ge 4$ there is a $2$-connected planar graph such that every path on $n$ vertices in it has a vertex of degree $k$.},

author = {Jendroľ, Stanislav},

journal = {Czechoslovak Mathematical Journal},

keywords = {planar graph; path; degree of vertices},

language = {eng},

number = {3},

pages = {481-490},

publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},

title = {Paths with restricted degrees of their vertices in planar graphs},

url = {http://eudml.org/doc/30500},

volume = {49},

year = {1999},

}

TY - JOUR

AU - Jendroľ, Stanislav

TI - Paths with restricted degrees of their vertices in planar graphs

JO - Czechoslovak Mathematical Journal

PY - 1999

PB - Institute of Mathematics, Academy of Sciences of the Czech Republic

VL - 49

IS - 3

SP - 481

EP - 490

AB - In this paper it is proved that every $3$-connected planar graph contains a path on $3$ vertices each of which is of degree at most $15$ and a path on $4$ vertices each of which has degree at most $23$. Analogous results are stated for $3$-connected planar graphs of minimum degree $4$ and $5$. Moreover, for every pair of integers $n\ge 3$, $ k\ge 4$ there is a $2$-connected planar graph such that every path on $n$ vertices in it has a vertex of degree $k$.

LA - eng

KW - planar graph; path; degree of vertices

UR - http://eudml.org/doc/30500

ER -

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