$F$-continuous graphs

Chartrand, Gary, et al. "$F$-continuous graphs." Czechoslovak Mathematical Journal 51.2 (2001): 351-361. <http://eudml.org/doc/30639>.

@article{Chartrand2001,
abstract = {For a nontrivial connected graph $F$, the $F$-degree of a vertex $v$ in a graph $G$ is the number of copies of $F$ in $G$ containing $v$. A graph $G$ is $F$-continuous (or $F$-degree continuous) if the $F$-degrees of every two adjacent vertices of $G$ differ by at most 1. All $P_3$-continuous graphs are determined. It is observed that if $G$ is a nontrivial connected graph that is $F$-continuous for all nontrivial connected graphs $F$, then either $G$ is regular or $G$ is a path. In the case of a 2-connected graph $F$, however, there always exists a regular graph that is not $F$-continuous. It is also shown that for every graph $H$ and every 2-connected graph $F$, there exists an $F$-continuous graph $G$ containing $H$ as an induced subgraph.},
author = {Chartrand, Gary, Jarrett, Elzbieta B., Saba, Farrokh, Salehi, Ebrahim, Zhang, Ping},
journal = {Czechoslovak Mathematical Journal},
keywords = {$F$-degree; $F$-degree continuous; -degree; -degree continuous},
language = {eng},
number = {2},
pages = {351-361},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {$F$-continuous graphs},
url = {http://eudml.org/doc/30639},
volume = {51},
year = {2001},
}

TY - JOUR
AU - Chartrand, Gary
AU - Jarrett, Elzbieta B.
AU - Saba, Farrokh
AU - Salehi, Ebrahim
AU - Zhang, Ping
TI - $F$-continuous graphs
JO - Czechoslovak Mathematical Journal
PY - 2001
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 51
IS - 2
SP - 351
EP - 361
AB - For a nontrivial connected graph $F$, the $F$-degree of a vertex $v$ in a graph $G$ is the number of copies of $F$ in $G$ containing $v$. A graph $G$ is $F$-continuous (or $F$-degree continuous) if the $F$-degrees of every two adjacent vertices of $G$ differ by at most 1. All $P_3$-continuous graphs are determined. It is observed that if $G$ is a nontrivial connected graph that is $F$-continuous for all nontrivial connected graphs $F$, then either $G$ is regular or $G$ is a path. In the case of a 2-connected graph $F$, however, there always exists a regular graph that is not $F$-continuous. It is also shown that for every graph $H$ and every 2-connected graph $F$, there exists an $F$-continuous graph $G$ containing $H$ as an induced subgraph.
LA - eng
KW - $F$-degree; $F$-degree continuous; -degree; -degree continuous
UR - http://eudml.org/doc/30639
ER -