Oriented Trees in Subquadratic Bound for Burr's Conjecture
The authors provide a subquadratic bound for Burr's conjecture, showing the universality of oriented trees in directed graphs with high chromatic numbers.
Secure Total Domination Number in Maximal Outerplanar Graphs
The author establishes upper and lower bounds for the secure total domination number in maximal outerplanar graphs, proving that these bounds are sharp.
Analyzing the Minimum Arcs in Oriented Graphs with Weak Diameter 2
The author explores the minimum number of arcs in oriented graphs with weak diameter 2, focusing on their properties and relationships to absolute oriented cliques.
K2-hypohamiltonian Graphs: Generation and New Families
K2-hypohamiltonian graphs can be exhaustively generated and new families can be created through an amalgamation operation, preserving key properties.
Insights on Highly Connected K2,ℓ-Minor Free Graphs
Highly connected K2,ℓ-minor free graphs have bounded size.
Oriented trees in O(k√k)-chromatic digraphs, a subquadratic bound for Burr's conjecture
Every oriented tree of order k is (8q2/15k√k + 11/3k + q5/6√k + 1)-universal.
Hadwiger's Conjecture and Coloring Small Graphs
Linear Hadwiger’s Conjecture reduced to coloring small graphs.
K2-hypohamiltonian Graphs: Generation and Families
K2-hypohamiltonian graphs can be exhaustively generated and new families can be created through specific operations.
Chordal Circular-arc Graphs Characterization
Identifying minimal split graphs not in the circular-arc class.
Hadwiger's Conjecture and Coloring Small Graphs
Linear Hadwiger's Conjecture reduced to coloring small graphs.
