- Tytuł:
- On the crossing numbers of join products of $W_4 + P_n$ and $W_4 + C_n$
- Autorzy:
-
Stas, Michal
Valiska, Juraj - Powiązania:
- https://bibliotekanauki.pl/articles/1397319.pdf
- Data publikacji:
- 2021
- Wydawca:
- Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
- Tematy:
-
graph
crossing number
join product
cyclic permutation
path
cycle - Opis:
- The crossing number cr(G) of a graph G is the minimum number of edge crossings over all drawings of G in the plane. The main aim of the paper is to give the crossing number of the join product $W_4 + P_n$ and $W_4 + C_n$ for the wheel $W_4$ on five vertices, where $P_n$ and $C_n$ are the path and the cycle on n vertices, respectively. Yue et al. conjectured that the crossing number of $W_m + C_n$ is equal to $Z(m+1)Z(n)+(Z(m)-1)[n/2]+n+[m/2]+2$, for all m,n ≥ 3, and where the Zarankiewicz’s number $Z(n)=[n/2][{n-1}/2]$ is defined for n ≥ 1. Recently, this conjecture was proved for $W_3 + C_n$ by Klesc. We establish the validity of this conjecture for $W_4 + C_n$ and we also offer a new conjecture for the crossing number of the join product $W_m + P_n$ for m ≥ 3 and n ≥ 2.
- Źródło:
-
Opuscula Mathematica; 2021, 41, 1; 95-112
1232-9274
2300-6919 - Pojawia się w:
- Opuscula Mathematica
- Dostawca treści:
- Biblioteka Nauki
Artykuł