Results 31 to 40 of about 10,088 (246)
Graphs with small diameter determined by their $D$-spectra [PDF]
, 2018 Let $G$ be a connected graph with vertex set $V(G)=\{v_{1},v_{2},...,v_{n}\}$. The distance matrix $D(G)=(d_{ij})_{n\times n}$ is the matrix indexed by the vertices of $G,$ where $d_{ij}$ denotes the distance between the vertices $v_{i}$ and $v_{j ...
Liu, Ruifang, Xue, Jie
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Hereditary Equality of Domination and Exponential Domination in Subcubic Graphs
Discussiones Mathematicae Graph Theory, 2021 Let γ(G) and γe(G) denote the domination number and exponential domination number of graph G, respectively. Henning et al., in [Hereditary equality of domination and exponential domination, Discuss. Math. Graph Theory 38 (2018) 275–285] gave a conjecture:
Chen Xue-Gang, Wang Yu-Feng, Wu Xiao-Fei
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Forbidden subgraphs in connected graphs
Theoretical Computer Science, 2004 Given a set $ =\{H_1,H_2,...\}$ of connected non acyclic graphs, a $ $-free graph is one which does not contain any member of $% $ as copy. Define the excess of a graph as the difference between its number of edges and its number of vertices. Let ${\gr{W}}_{k, }$ be theexponential generating function (EGF for brief) of connected $ $-free graphs ...
Ravelomanana, Vlady, Loÿs, Thimonier
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Clique minors in graphs with a forbidden subgraph [PDF]
Random Structures & Algorithms, 2021 AbstractThe classical Hadwiger conjecture dating back to 1940s states that any graph of chromatic number at least r has the clique of order r as a minor. Hadwiger's conjecture is an example of a well‐studied class of problems asking how large a clique minor one can guarantee in a graph with certain restrictions.
Jacob Fox +3 more
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Advice Complexity of the Online Induced Subgraph Problem [PDF]
, 2015 Several well-studied graph problems aim to select a largest (or smallest) induced subgraph with a given property of the input graph. Examples of such problems include maximum independent set, maximum planar graph, and many others.
Komm, Dennis +3 more
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Forbidden subgraphs, stability and hamiltonicity
Discrete Mathematics, 1999 The authors study the stability of some classes of claw-free graphs defined in terms of forbidden subgraphs under the closure operation defined in \textit{Z. Ryjáček} [J. Comb. Theory, Ser. B 70, No.~2, 217-224 (1997; Zbl 0872.05032)]. They characterize all connected graphs \(A\) such that the class of all \(CA\)-free graphs (where \(C\) denotes the ...
Jan Brousek +2 more
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Well-quasi-ordering versus clique-width : new results on bigenic classes. [PDF]
, 2016 Daligault, Rao and Thomassé conjectured that if a hereditary class of graphs is well-quasi-ordered by the induced subgraph relation then it has bounded clique-width.
A Atminas +21 more
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Coloring Graphs With Forbidden Almost Bipartite Subgraphs
Random Structures &Algorithms, Volume 66, Issue 4, July 2025.ABSTRACT Alon, Krivelevich, and Sudakov conjectured in 1999 that for every finite graph F$$ F $$, there exists a quantity c(F)$$ c(F) $$ such that χ(G)≤(c(F)+o(1))Δ/logΔ$$ \chi (G)\le \left(c(F)+o(1)\right)\Delta /\mathrm{log}\Delta $$ whenever G$$ G $$ is an F$$ F $$‐free graph of maximum degree Δ$$ \Delta $$. The largest class of connected graphs F$$
James Anderson +2 more
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Electronic Journal of Graph Theory and Applications, 2018 We find the structure of graphs that have no C4, $\overline{C}_4$, C5, S3, chair and co-chair as induced subgraphs. Then we deduce the structure of the graphs having no induced C4, $\overline{C_4}$, S3, chair and co-chair and the structure of the graphs ...
Salman Ghazal
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Discrete Mathematics & Theoretical Computer Science, 2018 We define a weakly threshold sequence to be a degree sequence $d=(d_1,\dots,d_n)$ of a graph having the property that $\sum_{i \leq k} d_i \geq k(k-1)+\sum_{i > k} \min\{k,d_i\} - 1$ for all positive $k \leq \max\{i:d_i \geq i-1\}$.
Michael D. Barrus
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