Span capacities of graphs
Mateja Gra\v{s}i\v{c}, Christopher Mouron, Aljo\v{s}a \v{S}uba\v{s}i\'c, Andrej Taranenko, Tanja Vojkovi\'c
TL;DR
This paper introduces the concept of d-capacity in graphs, determines its values for paths and cycles, and characterizes topfull graphs with maximum 1-capacity, linking to graph factorizations and connectivity.
Contribution
It defines d-capacity, computes exact values for specific graph classes, and characterizes topfull graphs, advancing understanding of graph traversal constraints.
Findings
d-capacity values for paths and cycles are determined
Bounds for bipartite graphs are provided
Topfull graphs are characterized and linked to factorizations
Abstract
The -capacity of a graph is introduced as the maximum number of players that can simultaneously traverse such that each player visits all vertices while maintaining a distance of at least under various movement rules. We determine their values for paths and cycles and provide bounds for bipartite graphs. Furthermore, we characterize topfull graphs, where the 1-capacities reach their theoretical maximum, establishing a connection to graph factorizations and connectivity.
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