The chromatic number of triangle-free and broom-free graphs in terms of the number of vertices
Sign Up to like & getrecommendations! Published in 2020 at "Aequationes mathematicae"
DOI: 10.1007/s00010-020-00760-z
Abstract: The Gárfás–Sumner conjecture asks whether for every tree T , the class of (induced) T -free graphs is $$\chi $$ χ -bounded. The conjecture is solved for several special trees, but it is still open… read more here.
Keywords: triangle free; free graphs; number; graph ... See more keywords
Independent Feedback Vertex Set for $$P_5$$P5-Free Graphs
Sign Up to like & getrecommendations! Published in 2018 at "Algorithmica"
DOI: 10.1007/s00453-018-0474-x
Abstract: The NP-complete problem Feedback Vertex Set is that of deciding whether or not it is possible, for a given integer $$k\ge 0$$k≥0, to delete at most k vertices from a given graph so that what remains… read more here.
Keywords: vertex set; free graphs; independent feedback; feedback vertex ... See more keywords
Connected Vertex Cover for $$(sP_1+P_5)$$(sP1+P5)-Free Graphs
Sign Up to like & getrecommendations! Published in 2019 at "Algorithmica"
DOI: 10.1007/s00453-019-00601-9
Abstract: The Connected Vertex Cover problem is to decide if a graph G has a vertex cover of size at most k that induces a connected subgraph of G. This is a well-studied problem, known to be NP-complete for restricted… read more here.
Keywords: problem; vertex cover; free graphs; connected vertex ... See more keywords
Random independent sets in triangle-free graphs
Sign Up to like & getrecommendations! Published in 2025 at "Forum of Mathematics, Sigma"
DOI: 10.1017/fms.2025.10112
Abstract: Abstract We establish several new results on the existence of probability distributions on the independent sets in triangle-free graphs where each vertex is present with a given probability. This setting was introduced and studied under… read more here.
Keywords: number; independent sets; sets triangle; triangle free ... See more keywords
Spanning trees of recursive scale-free graphs.
Sign Up to like & getrecommendations! Published in 2022 at "Physical review. E"
DOI: 10.1103/physreve.105.024312
Abstract: We present a link-by-link rule-based method for constructing all members of the ensemble of spanning trees for any recursively generated, finitely articulated graph, such as the Dorogovtsev-Goltsev-Mendes (DGM) net. The recursions allow for many large-scale… read more here.
Keywords: free graphs; trees recursive; scale free; graphs ... See more keywords
Hierarchical Sampling for the Visualization of Large Scale-Free Graphs.
Sign Up to like & getrecommendations! Published in 2022 at "IEEE transactions on visualization and computer graphics"
DOI: 10.1109/tvcg.2022.3201567
Abstract: Graph sampling frequently compresses a large graph into a limited screen space. This paper proposes a hierarchical structure model that partitions scale-free graphs into three blocks: the core, which captures the underlying community structure, the… read more here.
Keywords: degree nodes; scale free; structure; free graphs ... See more keywords
Triangle-free Graphs with Three Positive Eigenvalues
Sign Up to like & getrecommendations! Published in 2024 at "Algebra Colloquium"
DOI: 10.1142/s1005386724000397
Abstract: A graph [Formula: see text] is called triangle-free if [Formula: see text] does not contain any triangle as its induced subgraph. Let [Formula: see text] be the set of triangle-free graphs of order [Formula: see… read more here.
Keywords: three positive; see text; triangle free; formula see ... See more keywords
Bipartite (P6,C6)-Free Graphs: Recognition and Optimization Problems
Sign Up to like & getrecommendations! Published in 2024 at "Symmetry"
DOI: 10.3390/sym16040447
Abstract: The canonical decomposition of a bipartite graph is a new decomposition method that involves three operators: parallel, series, and K⨁ S . The class of weak-bisplit graphs is the class of totally decomposable graphs with respect… read more here.
Keywords: recognition; bipartite free; class; graphs ... See more keywords