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On a conjecture on the order of cages with a given girth pair

Author
Balbuena, C.; Salas, J.
Type of activity
Journal article
Journal
Discrete applied mathematics
Date of publication
2015-08-20
Volume
190-191
First page
24
Last page
33
DOI
https://doi.org/10.1016/j.dam.2015.03.020 Open in new window
Project funding
Control de invariantes en grafos sujetos a propiedades estructurales
Repository
http://hdl.handle.net/2117/78766 Open in new window
URL
http://www.sciencedirect.com/science/article/pii/S0166218X15001699 Open in new window
Abstract
A (k; g, h)-graph is a k-regular graph of girth pair (g, h) where g is the girth of the graph, h is the length of a smallest cycle of different parity than g and g < h. A (k; g, h)-cage is a (k; g, h)-graph with the least possible number of vertices denoted n(k; g, h). Harary and Kovacs (1983) conjectured the inequality n(k; g, h) <= n(k, h) for all k >= 3, g >= 3, h >= g + 1. In this paper, we prove this conjecture for all (k; g, h)-cage with g odd provided that a bipartite (k, h)-cage exists. ...
Citation
Balbuena, C., Salas, J. On a conjecture on the order of cages with a given girth pair. "Discrete applied mathematics", 20 Agost 2015, vol. 190-191, p. 24-33.
Keywords
Cages, Girth pair, ODD GIRTH, REGULAR GRAPHS, Regular graph
Group of research
COMBGRAPH - Combinatorics, Graph Theory and Applications

Participants