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$F$ -continuous graphs

Gary Chartrand, Elzbieta B. Jarrett, Farrokh Saba, Ebrahim Salehi, Ping Zhang (2001)

Czechoslovak Mathematical Journal

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...

Face size and the maximum genus of a graph. II: Nonsimple graphs

Yuanqiu Huang, Yan Pei Liu (2001)

Mathematica Slovaca

Few colored cuts or cycles in edge colored graphs

Jiří Matoušek (1988)

Commentationes Mathematicae Universitatis Carolinae

Fixed point results on a metric space endowed with a finite number of graphs and applications

Hajer Argoubi, Bessem Samet, Mihai Turinici (2014)

Czechoslovak Mathematical Journal

In this paper, we consider self-mappings defined on a metric space endowed with a finite number of graphs. Under certain conditions imposed on the graphs, we establish a new fixed point theorem for such mappings. The obtained result extends, generalizes and improves many existing contributions in the literature including standard fixed point theorems, fixed point theorems on a metric space endowed with a partial order and fixed point theorems for cyclic mappings.

Forte connexité des complexes polyèdraux

Peter Greenberg, Martin Loebl (1992/1993)

Séminaire de théorie spectrale et géométrie