Abstract
The circumference of a graph G is the length of a longest cycle in G , denoted by cir G . For any even number n , let c n = min { cir G | G is a 3-connected cubic triangle-free plane graph with n vertices}. In this paper, we show that an upper bound of c n is n + 1 − 3 ⌊ n / 136 ⌋ for n ≥ 136 .
Highlights
Graph theory has applications in various research areas
Similar to xy-path, a cycle of a graph G is defined as a sequence of distinct vertices u1, u2, . . . , um, u1 of G such that umu1, ujuj+1 ∈ E(G), for all j ∈ {1, 2, . . . , m − 1}. e triangle is a cycle of length 3, and a graph is triangle-free if it contains no triangle
A graph G is connected if there is a uv-path for all distinct u, v ∈ V(G)
Summary
Graph theory has applications in various research areas. In chemistry and biology, it gives an illustration of molecular structures in [1, 2], and it identifies interactions between humans and nature in [3]. Similar to xy-path, a cycle of a graph G is defined as a sequence of distinct vertices u1, u2, . In 1880, Tait [6] conjectured that a 3-connected cubic plane graph has a Hamilton cycle.
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
