Join of two graphs admits a nowhere-zero $3$-flow

Akbari, Saieed, et al. "Join of two graphs admits a nowhere-zero $3$-flow." Czechoslovak Mathematical Journal 64.2 (2014): 433-446. <http://eudml.org/doc/262039>.

@article{Akbari2014,
abstract = {Let $G$ be a graph, and $\lambda $ the smallest integer for which $G$ has a nowhere-zero $\lambda $-flow, i.e., an integer $\lambda $ for which $G$ admits a nowhere-zero $\lambda $-flow, but it does not admit a $(\lambda -1)$-flow. We denote the minimum flow number of $G$ by $\Lambda (G)$. In this paper we show that if $G$ and $H$ are two arbitrary graphs and $G$ has no isolated vertex, then $\Lambda (G \vee H) \le 3$ except two cases: (i) One of the graphs $G$ and $H$ is $K_2$ and the other is $1$-regular. (ii) $H = K_1$ and $G$ is a graph with at least one isolated vertex or a component whose every block is an odd cycle. Among other results, we prove that for every two graphs $G$ and $H$ with at least $4$ vertices, $\Lambda (G \vee H) \le 3$.},
author = {Akbari, Saieed, Aliakbarpour, Maryam, Ghanbari, Naryam, Nategh, Emisa, Shahmohamad, Hossein},
journal = {Czechoslovak Mathematical Journal},
keywords = {nowhere-zero $\lambda $-flow; minimum nowhere-zero flow number; join of two graphs; nowhere-zero $\lambda $-flow; minimum nowhere-zero flow number; join of two graphs},
language = {eng},
number = {2},
pages = {433-446},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Join of two graphs admits a nowhere-zero $3$-flow},
url = {http://eudml.org/doc/262039},
volume = {64},
year = {2014},
}

TY - JOUR
AU - Akbari, Saieed
AU - Aliakbarpour, Maryam
AU - Ghanbari, Naryam
AU - Nategh, Emisa
AU - Shahmohamad, Hossein
TI - Join of two graphs admits a nowhere-zero $3$-flow
JO - Czechoslovak Mathematical Journal
PY - 2014
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 64
IS - 2
SP - 433
EP - 446
AB - Let $G$ be a graph, and $\lambda $ the smallest integer for which $G$ has a nowhere-zero $\lambda $-flow, i.e., an integer $\lambda $ for which $G$ admits a nowhere-zero $\lambda $-flow, but it does not admit a $(\lambda -1)$-flow. We denote the minimum flow number of $G$ by $\Lambda (G)$. In this paper we show that if $G$ and $H$ are two arbitrary graphs and $G$ has no isolated vertex, then $\Lambda (G \vee H) \le 3$ except two cases: (i) One of the graphs $G$ and $H$ is $K_2$ and the other is $1$-regular. (ii) $H = K_1$ and $G$ is a graph with at least one isolated vertex or a component whose every block is an odd cycle. Among other results, we prove that for every two graphs $G$ and $H$ with at least $4$ vertices, $\Lambda (G \vee H) \le 3$.
LA - eng
KW - nowhere-zero $\lambda $-flow; minimum nowhere-zero flow number; join of two graphs; nowhere-zero $\lambda $-flow; minimum nowhere-zero flow number; join of two graphs
UR - http://eudml.org/doc/262039
ER -