Results 21 to 30 of about 4,536 (107)
Number of Subgraphs and Their Converses in Tournaments and New Digraph Polynomials
Journal of Graph Theory, Volume 110, Issue 2, Page 127-131, October 2025.ABSTRACT An oriented graph D is converse invariant if, for any tournament T, the number of copies of D in T is equal to that of its converse − D. El Sahili and Ghazo Hanna [J. Graph Theory 102 (2023), 684‐701] showed that any oriented graph D with maximum degree at most 2 is converse invariant. They proposed a question: Can we characterize all converse
Jiangdong Ai +4 more
wiley +1 more source
A Dichotomy Theorem for Γ‐Switchable H‐Colouring on m‐Edge‐Coloured Graphs
Journal of Graph Theory, Volume 110, Issue 2, Page 200-208, October 2025.ABSTRACT Let G be a graph in which each edge is assigned one of the colours 1 , 2 , … , m, and let Γ be a subgroup of S m. The operation of switching at a vertex x of G with respect to an element π of Γ permutes the colours of the edges incident with x according to π.
Richard Brewster +2 more
wiley +1 more source
Precedence‐Constrained Shortest Path
Networks, Volume 86, Issue 3, Page 282-295, October 2025.ABSTRACT We propose a variant of the shortest path problem where the order in which vertices occur in the path is subject to precedence constraints. Precedence constraints are defined in terms of vertex pairs (a,b)$$ \left(a,b\right) $$ which indicate that a vertex a$$ a $$ is the predecessor of a vertex b$$ b $$.
Christina Büsing +2 more
wiley +1 more source
Decremental Single-Source Reachability in Planar Digraphs
, 2017 In this paper we show a new algorithm for the decremental single-source reachability problem in directed planar graphs. It processes any sequence of edge deletions in $O(n\log^2{n}\log\log{n})$ total time and explicitly maintains the set of vertices ...
Italiano, Giuseppe F. +3 more
core +2 more sources
Networks, Volume 86, Issue 3, Page 325-357, October 2025.ABSTRACT The Minimum Path Cover (MPC) problem consists of finding a minimum‐cardinality set of node‐disjoint paths that cover all nodes in a given graph. We explore a variant of the MPC problem on directed acyclic graphs (DAGs) where, given a subset of arcs, each path within the MPC should contain at least one arc from this subset.
Nour ElHouda Tellache, Roberto Baldacci
wiley +1 more source
Approximating the Minimum Equivalent Digraph
, 2002 The MEG (minimum equivalent graph) problem is, given a directed graph, to find a small subset of the edges that maintains all reachability relations between nodes. The problem is NP-hard.
Balaji Raghavachari +7 more
core +1 more source
Journal of Graph Theory, Volume 110, Issue 1, Page 82-91, September 2025.ABSTRACT An inversion of a tournament T is obtained by reversing the direction of all edges with both endpoints in some set of vertices. Let inv k ( T ) be the minimum length of a sequence of inversions using sets of size at most k that result in the transitive tournament.
Raphael Yuster
wiley +1 more source
The Generic Circular Triangle‐Free Graph
Journal of Graph Theory, Volume 109, Issue 4, Page 426-445, August 2025.ABSTRACT In this article, we introduce the generic circular triangle‐free graph C 3 and propose a finite axiomatization of its first‐order theory. In particular, our main results show that a countable graph G embeds into C 3 if and only if it is a { K 3 , K 1 + 2 K 2 , K 1 + C 5 , C 6 }‐free graph.
Manuel Bodirsky, Santiago Guzmán‐Pro
wiley +1 more source
Countable connected-homogeneous digraphs [PDF]
, 2013 A digraph is connected-homogeneous if every isomorphism between two finite connected induced subdigraphs extends to an automorphism of the whole digraph.
Hamann, Matthias
core
On the Terwilliger Algebra of the Group Association Scheme of the Symmetric Group Sym ( 7 )
Journal of Combinatorial Designs, Volume 33, Issue 7, Page 261-274, July 2025.ABSTRACT Terwilliger algebras are finite‐dimensional semisimple algebras that were first introduced by Paul Terwilliger in 1992 in studies of association schemes and distance‐regular graphs. The Terwilliger algebras of the conjugacy class association schemes of the symmetric groups Sym ( n ), for 3 ≤ n ≤ 6, have been studied and completely determined ...
Allen Herman +2 more
wiley +1 more source