χ-boundedness and related problems on graphs without long induced paths: A survey
A Char, T Karthick - Discrete Applied Mathematics, 2025 - Elsevier
Given a hereditary class of graphs G, a function f: N→ N such that f (1)= 1 and f (x)≥ x, for all
x∈ N is a χ-binding function for G if χ (G)≤ f (ω (G)), for each G∈ G. The class G is called χ …
x∈ N is a χ-binding function for G if χ (G)≤ f (ω (G)), for each G∈ G. The class G is called χ …
Optimal chromatic bound for (P 2+ P 3, P 2+ P 3¯ P_2+P_3,̄P_2+P_3)‐free graphs
A Char, T Karthick - Journal of Graph Theory, 2024 - Wiley Online Library
For a graph GG, let χ (G) χ(G) (ω (G) ω(G)) denote its chromatic (clique) number. AP 2+ P 3
P_2+P_3 is the graph obtained by taking the disjoint union of a two‐vertex path P 2 P_2 and …
P_2+P_3 is the graph obtained by taking the disjoint union of a two‐vertex path P 2 P_2 and …
A Tight Linear Bound to the Chromatic Number of -Free Graphs
W Dong, B Xu, Y Xu - Graphs and Combinatorics, 2023 - Springer
Let F 1 and F 2 be two disjoint graphs. The union F 1∪ F 2 is a graph with vertex set V (F
1)∪ V (F 2) and edge set E (F 1)∪ E (F 2), and the join F 1+ F 2 is a graph with vertex set V …
1)∪ V (F 2) and edge set E (F 1)∪ E (F 2), and the join F 1+ F 2 is a graph with vertex set V …
-binding functions for some classes of -free graphs
The class of $2 K_2 $-free graphs have been well studied in various contexts in the past. It is
known that the class of $\{2K_2, 2K_1+ K_p\} $-free graphs and $\{2K_2,(K_1\cup K_2)+ …
known that the class of $\{2K_2, 2K_1+ K_p\} $-free graphs and $\{2K_2,(K_1\cup K_2)+ …
Colouring graphs with no induced six-vertex path or diamond
J Goedgebeur, S Huang, Y Ju, O Merkel - International Computing and …, 2021 - Springer
The diamond is the graph obtained by removing an edge from the complete graph on 4
vertices. A graph is (P_6 P 6, diamond)-free if it contains no induced subgraph isomorphic to …
vertices. A graph is (P_6 P 6, diamond)-free if it contains no induced subgraph isomorphic to …
THE CHROMATIC NUMBER OF-FREE GRAPHS
K Lan, Y Zhou, F Liu - Bulletin of the Australian Mathematical Society, 2023 - cambridge.org
THE CHROMATIC NUMBER OF (P6, C4, diamond)-FREE GRAPHS Page 1 Bull. Aust. Math.
Soc. 108 (2023), 1–10 doi:10.1017/S0004972722001034 THE CHROMATIC NUMBER OF (P6 …
Soc. 108 (2023), 1–10 doi:10.1017/S0004972722001034 THE CHROMATIC NUMBER OF (P6 …
Colouring graphs with no induced six-vertex path or diamond
J Goedgebeur, S Huang, Y Ju, O Merkel - Theoretical Computer Science, 2023 - Elsevier
The diamond is the graph obtained by removing an edge from the complete graph on 4
vertices. A graph is (P 6, diamond)-free if it contains no induced subgraph isomorphic to a …
vertices. A graph is (P 6, diamond)-free if it contains no induced subgraph isomorphic to a …
On graphs with no induced bull and no induced diamond
S Mishra - arXiv preprint arXiv:2107.03750, 2021 - arxiv.org
A bull is the graph obtained by adding two pendant edges at different vertices of a triangle. A
diamond is the graph obtained from a $ K_4 $ by deleting an edge. In this paper, we study …
diamond is the graph obtained from a $ K_4 $ by deleting an edge. In this paper, we study …
Structure of some (P7, C4)-free graphs with application to colorings
R Chen, D Wu, B Xu - Discrete Applied Mathematics, 2024 - Elsevier
We use P t and C t to denote a path and a cycle on t vertices, respectively. A diamond is a
graph obtained from two triangles that share exactly one edge. A kite is a graph that consists …
graph obtained from two triangles that share exactly one edge. A kite is a graph that consists …
Optimal chromatic bound for (, )-free graphs
A Char, T Karthick - arXiv preprint arXiv:2205.07447, 2022 - arxiv.org
For a graph $ G $, let $\chi (G) $($\omega (G) $) denote its chromatic (clique) number. A $
P_2+ P_3 $ is the graph obtained by taking the disjoint union of a two-vertex path $ P_2 …
P_2+ P_3 $ is the graph obtained by taking the disjoint union of a two-vertex path $ P_2 …