Related papers: Evolutionary Hamiltonian Graph Theory
A hamiltonian cycle system (HCS, for short) of a graph $\Gamma$ is a partition of the edges of $\Gamma$ into hamiltonian cycles. A HCS is cyclic when it is invariant under a cyclic permutation of all the vertices of $\Gamma$; the existence…
We propose a model for the evolutionary ecology of words as one attempt to extend evolutionary game theory and agent-based models by utilizing the rich linguistic expressions of Large Language Models (LLMs). Our model enables the emergence…
Game theory is one of the key paradigms behind many scientific disciplines from biology to behavioral sciences to economics. In its evolutionary form and especially when the interacting agents are linked in a specific social network the…
We initiate the study of Hamiltonian cycles up to symmetries of the underlying graph. Our focus lies on the extremal case of Hamiltonian-transitive graphs, i.e., Hamiltonian graphs where, for every pair of Hamiltonian cycles, there is a…
In the realm of evolutionary game theory, standard frameworks typically presuppose that every player possesses comprehensive knowledge and unrestricted access to the entire strategy space. However, real-world human society inherently…
We present a new method to calculate formation of cosmological structure in the Newtonian limit. The method is based on Lagrangian perturbation theory plus two key theoretical extensions. One advance involves identifying and fixing a…
The standard Large Deviation Theory (LDT) mirrors the Boltzmann-Gibbs (BG) factor which describes the thermal equilibrium of short-range Hamiltonian systems, the velocity distribution of which is Maxwellian. It is generically applicable to…
Understanding the influence of an environment on the evolution of its resident population is a major challenge in evolutionary biology. Great progress has been made in homogeneous population structures while heterogeneous structures have…
Motivated by a relaxed notion of the celebrated Hamiltonian cycle, this paper investigates its variant, parity Hamiltonian cycle (PHC): A PHC of a graph is a closed walk which visits every vertex an odd number of times, where we remark that…
In this paper, the concept of cyclic subsets in graph theory is introduced. An interesting theorem which relates to the collective Hamiltonicity of these cyclic subsets in graphs is also presented. This paper uses this theorem to construct…
We have generalized our ``unified'' model of evolutionary ecology by taking into account the possible movements of the organisms from one ``patch'' to another within the same eco-system. We model the spatial extension of the eco-system…
Evolutionary game dynamics is one of the most fruitful frameworks for studying evolution in different disciplines, from Biology to Economics. Within this context, the approach of choice for many researchers is the so-called replicator…
In this paper we prove a sufficient condition for the existence of a Hamilton cycle, which is applicable to a wide variety of graphs, including relatively sparse graphs. In contrast to previous criteria, ours is based on only two…
Motivated by interpretability and reliability, we investigate whether large language models (LLMs) deploy universal geometric structures to encode discrete, graph-structured knowledge. To this end, we present two complementary experimental…
The evolution of the biosphere unfolds as a luxuriant generative process of new living forms and functions. Organisms adapt to their environment, exploit novel opportunities that are created in this continuous blooming dynamics. Affordances…
In earlier work, we have developed a nonequilibrium statistical field theory description of cosmic structure formation, dubbed Kinetic Field Theory (KFT), which is based on the Hamiltonian phase-space dynamics of classical particles and…
Let $\mathcal{G}(k)$ denote the set of connected $k$-regular graphs $G$, $k\geq2$, where the number of vertices at distance 2 from any vertex in $G$ does not exceed $k$. Asratian (2006) showed (using other terminology) that a graph…
Here we postulate three laws which form a mathematical framework to capture the essence of Darwinian evolutionary dynamics. The second law is most quantitative and is explicitly expressed by a unique form of stochastic differential…
We analyse the unreduced, nonperturbative dynamics of an arbitrary many-body interaction process with the help of the generalised effective potential method and reveal the well-specified universal origin of change (emergence), time and…
Kronk introduced the $l$-path hamiltonianicity of graphs in 1969. A graph is $l$-path Hamiltonian if every path of length not exceeding $l$ is contained in a Hamiltonian cycle. We have shown that if $P=uvz$ is a 2-path of a 2-connected,…