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All Journal Electronic Journal of Graph Theory and Applications (EJGTA)
Zhiguo Li
Department of Mathematics, Hebei University of Technology, China
Electrical & Electronics Engineering

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The Alon-Tarsi number of two kinds of planar graphs Zhiguo Li; Qing Ye; Zeling Shao
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 11, No 1 (2023): Electronic Journal of Graph Theory and Applications
Publisher : GTA Research Group, Univ. Newcastle, Indonesian Combinatorics Society and ITB

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.5614/ejgta.2023.11.1.13

Abstract

The Alon-Tarsi number AT(G) of a graph G is the least k for which there is an orientation D of G with max outdegree k − 1 such that the number of spanning Eulerian subgraphs of G with an even number of edges differs from the number of spanning Eulerian subgraphs with an odd number of edges. In this paper, the exact value of the Alon-Tarsi number of two kinds of planar graphs is obtained.
The matching book embeddings of pseudo-Halin graphs Zeling Shao; Yanling Hu; Huiru Geng; Zhiguo Li
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 11, No 1 (2023): Electronic Journal of Graph Theory and Applications
Publisher : GTA Research Group, Univ. Newcastle, Indonesian Combinatorics Society and ITB

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.5614/ejgta.2023.11.1.23

Abstract

The book embedding of a graph G is to arrange the set of points of the graph on a line (spine) and embed the edges on the half-plane bounded by the spine so that the edges in the same page do not intersect with each other. If the maximum degree of vertices in each page is 1, the book embedding is matching book embedding. The matching book thickness of G is the minimum number n that G can be matching book embedded in n-page. In this paper, the matching book thickness of pseudo-Halin graphs is determined.
Co-Authors Huiru Geng Qing Ye Yanling Hu Zeling Shao