Fractional arboricity, strength, and principal partitions in graphs and matroids

DOI10.1016/0166-218X(92)90002-RzbMath0773.05033OpenAlexW2074890468MaRDI QIDQ1208447

Arthur M. Hobbs, Paul A. Catlin, Jerrold W. Grossman, Hong-Jian Lai

Publication date: 16 May 1993

Published in: Discrete Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0166-218x(92)90002-r

zbMATH Keywords

strengthmatroidfractional arboricityprincipal partition

Mathematics Subject Classification ID

Combinatorial aspects of matroids and geometric lattices (05B35) Graph theory (05C99)

Related Items (38)

Extensions of matroid covering and packing ⋮ Fractional spanning tree packing, forest covering and eigenvalues ⋮ Strength and fractional arboricity of complementary graphs ⋮ Every matroid is a submatroid of a uniformly dense matroid ⋮ Spanning Rigid Subgraph Packing and Sparse Subgraph Covering ⋮ Balanced and 1-balanced graph constructions ⋮ A property on reinforcing edge-disjoint spanning hypertrees in uniform hypergraphs ⋮ Digraph analogues for the Nine Dragon Tree Conjecture ⋮ Group Connectivity, Strongly Z_m-Connectivity, and Edge Disjoint Spanning Trees ⋮ Supereulerian regular matroids without small cocircuits ⋮ Cyclic orderings and cyclic arboricity of matroids ⋮ Graph rigidity properties of Ramanujan graphs ⋮ Supereulerian graphs in the graph family \(C_{2}(6,k)\) ⋮ Arboricity games: the core and the nucleolus ⋮ Cyclically orderable generalized Petersen graphs ⋮ Chvátal-Erdős conditions and almost spanning trails ⋮ Degree sequences and graphs with disjoint spanning trees ⋮ Spanning cycles in regular matroids without small cocircuits ⋮ Spanning trees: A survey ⋮ Packing branchings under cardinality constraints on their root sets ⋮ Fractional arboricity, strength and eigenvalues of graphs with fixed girth or clique number ⋮ Characterizations of strength extremal graphs ⋮ Decomposing a graph into pseudoforests with one having bounded degree ⋮ Decomposing a graph into forests and a matching ⋮ Brick partitions of graphs ⋮ Degree conditions for group connectivity ⋮ Duality in graph families ⋮ A proof of the molecular conjecture ⋮ Characterization of removable elements with respect to having \(k\) disjoint bases in a matroid ⋮ Decomposing a graph into forests: the nine dragon tree conjecture is true ⋮ Edge-disjoint spanning trees and forests of graphs ⋮ Transforming a graph into a 1-balanced graph ⋮ Edge-connectivity and edge-disjoint spanning trees ⋮ Decomposing a graph into forests ⋮ Unnamed Item ⋮ Degree sequence realizations with given packing and covering of spanning trees ⋮ Ons-Hamiltonian Line Graphs ⋮ Vulnerability issues of star graphs, alternating group graphs and split-stars: Strength and toughness

Cites Work

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• The principal minors of a matroid
• Connectivity and edge-disjoint spanning trees
• On the Problem of Decomposing a Graph into n Connected Factors
• Edge-Disjoint Spanning Trees of Finite Graphs
• Activities on circuit theory in Japan
• Optimal attack and reinforcement of a network
• Strongly balanced graphs and random graphs
• A Solution of the Shannon Switching Game
• Lehmans switching game and a theorem of Tutte and Nash-Williams
• PRINCIPAL PARTITION AND PRINCIPAL MINORS OF A MATROID, WITH APPLICATIONS†
• Decomposition of Finite Graphs Into Forests

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